If you play with more than one player, you have to restart the sing-mode, if you want to have another name ...
Could the name maybe enter after singing:
Name of Singer 1:
Name of Singer 2:
Maybe with an Option => Enter name after Singing YES-NO
Logged In: NO
That would be great.
Maybe just type in the name if you get to the high-score list.
We often use ultrastar at partys and then you don't want to change the name all the name so we use the same name all the time. But it make's a very boring high-score list.
When singing on a party it is not always clear upfront who wants to sing, and "organizing" and going back to the previous menu spoils the fun...
You can still change players without going back to the previous menu. You can do it by changing profiles from the song selection screen.