The name change is aimed at reflecting the growing dominance of its American operations, which trade under that brand at hundreds of grocery store counters.
Snowfox is majority-owned by Mayfair Equity Partners, the London-based private equity firm.
Having started life as the first conveyer-belt sushi brand in Britain, YO! has established itself as the leading multinational Japanese food business, selling more than 60m trays of sushi annually.
People close to the company said it was growing at double the rate of the wider market, and now supplies retailers such as Tesco and Waitrose in the UK, and Kroger and Loblaws in North America.
It distributes fresh pre-packaged Japanese food to more than 3,700 food-service and grocery outlets.
In contrast, it now operates only 65 restaurants, having shuttered 19 sites last year as part of a restructuring to keep it afloat.
The potential flotation of the business is expected to take place in London, despite the growing share of revenues generated by its US arm.
The company, which is run by chief executive Richard Hodgson, has appointed the former Argos chief John Walden as chairman, with former Whitbread finance director Chris Rogers also joining the group’s board.
Since its initial investment in YO! in 2015, Mayfair has helped to orchestrate the takeover of Canada’s Bento Sushi and a merger with SnowFox in the US last year.
Snowfox will retain the YO! name for its restaurants and food-to-go operations.