Aren't people allowed to change their names in the US? In the UK one can change one's name as often as one wishes (by deed poll), as far as I am aware.
Yes. Indeed, my understanding is that by common-law tradition, you can even use a new assumed name without any official paperwork at all, as long as you're not using it with intent to defraud someone.
This of course runs into problems with modern bureaucratic assumptions, and so there are also ways to change one's name very officially as well, and register the change with all the entities requiring continuity-of-recordkeeping.