Instead of making multiple windows, you could make a single window and then create 2 functions, 1 for the game and the other for registration. Then at start, you could call the registration function and then, the game function. You have not given any code or anything, so we can't help you a lot...
there is a task: you need to write a registration menu program. it is necessary to do this necessarily on pygame. no other way. how can this be implemented at all? as I know, pygame does not support multi-window. how to do it then?
menu registration in pygame