Richard B had long expressed a desire to have an airline with the Virgin name in the USA. In 2005-ish they started working on plans for Virgin USA, which became Virgin America.
The plan was to launch out of San Francisco and go head-to-head with the biggest established competitors on trains-continental routes and on west coast trunk routes (LAX, etc).
They found investors and filed the paperwork, but the US Department of Transport denied the application. Basically the USA is a closed market to foreign competition, and the US unions and airlines campaigned vigorously against Virgin Group having a controlling stake in the airline. So they restructured the company, removed Branson and some UK directors from the board, and created a US-held trust. The airline was technically American but Virgin (as usual) got a lot of money for branding and corporate services.
To answer your question - in its core markets, Virgin America was very popular. Because US airlines tend to own or lease the gates at airports, they were able to do a lot more to make the whole kerbside to gate experience special. Lounges were built, the cabin interiors were ahead of the competition, and if I’m not mistaken they also pioneered the use of at-seat ordering for food and beverages. They were also first to roll out inflight WiFi across their whole fleet (brand new Airbus, built in the USA of course).
The airline went public in 2014, and because share holders are generally after a quick buck, there was immediately a lot of interest in an acquisition or merger. Alaska Airlines (who are stronger outside their home state than the name suggests, especially down the west coast) and JetBlue fought it out, and Alaska won. The airlines, fleets, routes and staff merged and the name was dropped.
Aside from the record label and a few shops, that’s the biggest exposure the Virgin brand has in America. It was popular with a few niche markets, especially California’s tech and showbiz industries, who benefited a lot from the fresh competition it brought to California and trans-con flying. But in the rest of the USA, the brand was probably equally if not more associated with the initial disputes about a foreign owned company breaking in to the domestic market.