SAN FRANCISCO  — The CEO of Netflix said he was sorry for mishandling a recent price increase that caused customers to cancel the service in droves. But the apology was drowned out by a decision that angered subscribers all over again.

The company will split into two services — one with an odd new name that offers the familiar discs in red envelopes and another for online streaming of TV shows and movies.

The DVD service will be called Qwikster, a name that is supposed to signify a commitment to fast service but quickly became an object of ridicule Monday on the Internet. The streaming service will keep the Netflix name.

Netflix, which had 24.6 million U.S. subscribers at the end of June and is the nation’s largest video subscription service, redefined home entertainment over the past decade with its DVDs by mail. Now it’s trying to prepare for the day when watching movies on a disc goes the way of driving to the video store to pick up a VHS tape.

But lately, it has bungled the transition. The company has lost half its market value since July, when it announced that customers who wanted DVDs and streaming had to pay for them separately — and pay up to 60 percent more.

The decision to rebrand the best-known part of Netflix’s business left some experts wondering whether CEO Reed Hastings is losing the touch that established him as an influential figure in technology and entertainment.

Others see the logic in trying to make sure Netflix keeps a thriving business as customers abandon DVDs and shift in greater numbers to beaming movies and TV shows into their living rooms over high-speed Internet connections.

It’s going to be a painful transition, as Hastings acknowledged as he cut loose the DVD service.

“It’s hard for me to write this after over 10 years of mailing DVDs with pride, but we think it is necessary and best,” Hastings wrote on a Netflix blog. The CEO of the rechristened Qwikster service will be Andy Rendich, a longtime Netflix employee.

Hastings found little sympathy among the more than 10,000 people who commented on the blog posting.

Most of them lambasted him for making life more difficult for about 12 million customers who get both streaming and DVD rentals. Those people will have to visit two websites to make requests and update their billing information.

Other critics questioned the sincerity of his apology for the recent price increase and ripped him for giving DVD rentals a different identity — and for the name Qwikster in particular.

“It’s a really dumb name,” said Scott Devine of Burbank, Calif., who dropped the DVD service after the price increase was announced two months ago. “You would think they would choose something that at least had ‘flick” in the name.”

The split may seem like the natural next step to Hastings, but he appears tone deaf to subscribers, said John Tschohl, president of the Service Quality Institute, a consulting service, and author of the book “Achieving Excellence Through Customer Service.”

“I don’t think Netflix is listening to its customers at all,” he said. “They have really blown it.”