Kip Moore, a country music singer-songwriter with hits like “Beer Money” and “Hey Pretty Girl,” has had some disturbing experiences with fans lately.

At some shows, women have approached him demanding to know why he stopped chatting with them on Instagram or Facebook. Some said they left their husbands to be with him after he said he loved them. Now they could be together, the women told him.

“They’re handing me a letter, you know, ‘Here’s the divorce papers. I’ve left so and so,’” Mr. Moore, 38, said. “If I check my inbox right now, I’d have hundreds of these messages. But I try not to check it, because it disheartens me.”

Mr. Moore, fueled by his country music fame, is a victim of what has become a widespread phenomenon: identity theft on social media. Recent searches found at least 28 accounts impersonating him on Facebook and at least 61 on Instagram. Many of the accounts send messages to his fans promising love and asking for money. Those who get duped often direct their anger at the real Mr. Moore.

Read more from The New York Times:

How fake Mark Zuckerbergs scam Facebook users out of their cash

On social media, lax enforcement lets impostor accounts thrive

Facebook says it’s policing fake accounts. But they’re still easy to spot

The issue of fake social media accounts masquerading as public figures is acute. Facebook, Instagram and Twitter teem with accounts that mimic ordinary people to spread propaganda or to be sold as followers to those who want to appear more influential. But millions of the phony profiles pose specifically as actors, singers, politicians and other well-known figures to broadcast falsehoods, cheat people out of money — or worse. Last year, Australian authorities charged a 42-year-old man with more than 900 child sex offenses for impersonating Justin Bieber on Facebook and other sites to solicit nude photos from minors.

The sheer volume of social media impostors poses a challenge to even the wealthiest celebrities. In a video last year, Oprah Winfrey warned her Twitter followers that “somebody out there is trying to scam you using my name and my avatar on social media, asking for money.”

It was an unusual step. Harriet Seitler, chief marketing officer for the Oprah Winfrey Network, said her team only reports Ms. Winfrey’s social media impersonators that try to sell tickets to shows or to solicit donations when they gain traction.

“There’s way too many to try to actively police them day in and day out,” Ms. Seitler said.

Even Facebook’s top executives, including Mark Zuckerberg, have struggled with impersonators.

To get a sense of the scale of the problem, The New York Times commissioned an analysis to tally the number of impersonators across social media for the 10 most followed people on Instagram, including Beyoncé and Taylor Swift. The analysis, conducted by Social Impostor, a firm that protects celebrities’ names online, found nearly 9,000 accounts across Facebook, Instagram and Twitter pretending to be those 10 people.

Brazilian soccer player Neymar was the subject of the most fake accounts, 1,676. Pop star Selena Gomez was second, with 1,389, according to the analysis, which was completed in April and did not count explicit parody or fan pages. Beyoncé had 714 impersonators; Ms. Swift had 233, the least among the group.

Twitter, Instagram and Facebook have compounded the problem with lax enforcement of their own policies prohibiting impersonators. Some people who report such accounts said the sites had gotten better at removing them, but others said the companies did not police them adequately. Most people agreed that once the sites erased the accounts, they did little to keep those behind them from creating new ones.

“It’s just a Band-Aid,” Mr. Moore said.

Facebook and its Instagram unit said they were cracking down on fake accounts. The social network said it had recently added software that automatically detected impostors and frauds, which it used to remove more than one million accounts since March.

Yet in April, tucked away in the fine print of an earnings document, Facebook increased its estimate of fake accounts on the site by 20 million — to as many as 80 million accounts, or about 4 percent of the total number of accounts. The company said the site’s sheer size made it difficult to measure the problem.

“Facebook and Instagram are really powerful ways to connect, and because of that, you have no shortage of people trying to use those systems in nefarious ways,” said Scott Dickens, a Facebook product manager who develops tools to fight hoaxes. “Those sets of people will continue to get smarter to evade detection capabilities that we put in place.”

How easy is it to impersonate someone online? To find out, I created my own impostors.

For those at home: I do not recommend doing this. Making fake social media accounts, even of yourself, is forbidden by the companies’ terms of service. After I made the accounts, I also informed the companies so that the profiles could be removed.

Making the duplicate accounts turned out to be a breeze. I created eight Facebook accounts in one hour last week that purported to be me, using my exact name and job title and a photo pulled from my verified profile. All that was required was a different email address for each account. (Email addresses are free and plentiful on the internet.)

On the fifth account, Facebook blocked me from using my name. I thought the jig was up. Then I added a middle initial, and the profile was approved. Later, I deleted the middle initial. After I had created eight fake accounts, Facebook began requiring a phone number. So I waited a few days and then created three more.

The fake accounts were live for five days before I reported them via Facebook’s site. The company removed them all within minutes.

I used many of the same email addresses to construct Instagram impostors of myself. Instagram made it trickier, sometimes requiring a phone number, which I never offered, or blocking me outright. But by using several different devices, like my wife’s phone, I eventually created 10 profiles with my name and bio and a photo pulled from my verified account.

I then reported the 10 accounts to Instagram. The photo-sharing site removed five after a day. The other five were still active more than four days later.

Twitter was better. After I successfully created one impostor, the company blocked me from using my actual profile photo on a second phony account. The company quickly removed the impersonator when I reported it.

I could have created many more accounts if I was willing to pay to do so. Dozens of websites reviewed by The Times sell bulk Facebook, Instagram and Twitter accounts. Scam artists can pick from detailed menus: accounts with friends, attached to phone numbers or with unique profile photos. Fake accounts that look more established and were typically created years ago, known as aged accounts, fetch $5 to $40 each.

And if you are ready to buy? The vendors accept Bitcoin.

For many celebrities, the flood of fake social media accounts can cause real-life headaches.

Trace Adkins, the country music singer, said he had encountered people at nearly every show who claimed that in online messages, he had promised them free tickets and a backstage tour.

“It’s just exasperating, because there doesn’t seem to be anything anybody can … ” he said in an interview on Thursday before a concert in Fayetteville, Ga., his voice trailing off. “My tour manager just walked on the bus and said it just happened.”

Women regularly tell Mr. Adkins he had proposed to them online. “I mean it’s off-the-charts crazy, man,” he said. “But people believe this stuff and we have to deal with it.”

When I messaged an Instagram account pretending to belong to Mr. Adkins, the impostor directed me to a profile impersonating the singer’s daughter. The account, which had posted numerous photos of the college-age Ms. Adkins, said she had started a charity and sent me a photo of a man in a hospital bed.

Whoever was behind the fake account then asked for a donation “to pay a dying man’s hospital bill.” The sum? $14,700. When I demurred, the impostor wrote snippily, “Are you willing to help us with money or what?”

Mr. Adkins said of the account posing as his daughter: “I would like to hunt that guy down and give him a beating.” He said his team had contacted the F.B.I. and the social media companies, to no avail.

“It falls on deaf ears,” he said. “They know there are hundreds of fake accounts and they don’t do anything about it.”

Last year, Mr. Adkins posted a video on Facebook warning fans of the online impostors. Last week, 20 other country and pop stars, including Kelly Clarkson and Blake Shelton, released a video urging fans to steer clear of imitators.

Mr. Moore said the fake accounts had weighed on him. He recently got a message from a man who said his wife was leaving him for Mr. Moore after she had started a relationship with the singer online. When he clicked on the woman’s profile, he found a 60-year-old mother of five.

“How can it not bother me?” Mr. Moore said. “I have people like, ‘You’re the biggest scumbag ever. You were doing this, messaging my mom or whatever.’ It’s a disheartening thing, when you’re viewed a certain way by people that has nothing to do with your character in real life.”

James Martin, a Jesuit priest and author with 571,000 followers on Facebook, said imitators sent messages to his followers soliciting donations or “they’ll start posting horrible things in my name,” like criticism of Catholic charities.

“There is a special place in hell reserved for people like that,” he said.

The comedian Dave Chappelle said he began following messages posted on Twitter by one of his impersonators and actually found them funny — until the account began to trade insults with the Twitter account of another comedian, Katt Williams.

“Katt Williams starts saying things to the fake Dave Chappelle that’s hurting the real Dave Chappelle’s feelings,” Mr. Chappelle recounted on “The Tonight Show” in 2014.

Mr. Chappelle said he was worried when he later encountered Mr. Williams at an event. Mr. Chappelle said he told Mr. Williams he did not have a Twitter account. “So?,” Mr. Williams replied. “That’s not unusual. I don’t have a Twitter page either.”

One of the social media companies’ main defenses against fake accounts is users, whom they ask to report suspicious activity. Facebook recently added an option to report profiles as impostors.

To conclude my experiment, I reported more than 30 celebrity impostor accounts to the companies — including all the examples cited in this article — to see what would happen.

I received responses to only six of those reports, all from Instagram. They included two Mr. Moore impersonators and a phony Ms. Winfrey, with 727 followers, which had posted images of sick and poor children and had asked for donations. Instagram said the accounts did not violate its policies. There was no option to appeal.

Instagram removed one account that I flagged, which impersonated Ms. Swift, although the company did not notify me.

“We take the reports really seriously,” said Pete Voss, a Facebook and Instagram spokesman, adding that the company would remove the other accounts I had reported. “We’re not going to get it 100 percent right every time obviously.”

Ian Plunkett, a Twitter spokesman, said the company had “strict policies and enforcement procedures” regarding impersonation, and he directed me to the company’s rules.

In total, Facebook said it had removed roughly 583 million fake accounts, most within minutes of creation, in January, February and March. Twitter said its software was identifying nearly 10 million “spammy or automated” accounts a week.

Mr. Dickens, the Facebook product manager, said the company was trying to stamp out every pretender but that the task was complicated by the social network’s size; the nuance of separating imitators from fan pages; and the sophistication of some of the impostors.

“It’s the arms race,” he said.

Facebook is fighting much of this arms race against people in West Africa. People who report bogus accounts said they had tracked many of the internet protocol addresses connected to them to Nigeria or Ghana, where those behind the fake accounts call themselves Yahoo Boys.

One Nigerian man who advertises training for Yahoo Boys said in a phone interview that Facebook had gotten better at removing impostors but that Instagram had not. The man, who declined to be identified because his activity could be criminal, said he had run romance schemes by impersonating young female celebrities like Ariana Grande and Victoria Justice.

Those schemes were not as lucrative as pretending to be another kind of celebrity, though. “Porn star is better,” he said.