I think they'd continue to refer to it as such but to me it feels a little odd. The "United Kingdom" was originally a union of the kingdoms of Scotland and England, the latter having already conquered and absorbed Wales. Losing one former-kingdom of that union and maintaining you're the "United Kingdom" feels a bit dishonest, a little bit "Democratic People's Republic ..." :)
"The Kingdom of England and Wales" makes more sense but "KEW" and "EW" sound odd as acronyms, and will just lead to most of the world referring to the place as "England" (as many in the USA currently do tbh). That is, if they decide to keep the monarchy...