Peter Thomas Roth, the founder and formulator of a cosmetics company that bears his name, said he had realized when he was starting his company in the early 1990s that it could take a week to come up with a name and two to three more weeks to check with the Patent Office to see if it had already been taken.

He remembered preparing for a trade show and needing a name, so he chose all three of his. He added the product’s ingredients and intended purpose on the label.

“At the beginning, there were no disadvantages or advantages because no one cared,” Mr. Roth said.

Occasionally, buyers wanted to meet him. “Sometimes, they’d want me there because I was the face of the brand,” he said. “It didn’t always work. They’d say, ‘Can Peter come?’ I’d say, ‘No, he can’t come to Ohio for a $1,000 order because the airfare and hotel cost more.’”

Early on, Mr. Roth learned the extent and limits of having the company named for him. “I can call the head of a company, and they actually take the call,” he said. What he could not do, though, was call the same company’s accounts payable department: “You can’t call a customer to ask for money. You look like a loser.”

For some entrepreneurs, their name is the only logical choice for a company.

Chris Kappler won gold and silver medals in equestrian events at the 2004 Olympic Games in Athens, which topped a career of some 100 horse-jumping victories on the Grand Prix circuit. He now runs Chris Kappler Inc., which helps people select and train horses and teaches riders of all levels in training facilities in New Jersey and Florida.

“If you took myself out of it, there isn’t much to it,” he said. “It’s a service business in a lot of ways.”