OMG RLY?
so why is it ok for Gabe to change his name but if someone else adapts the name Belmont you consider it "bad?"
Gabriel gave himself the Surname Belmont because as an orphan, he had NO surname. His being a Cronqvist bastard was merely a rumor. Cant be proven one way or another, and even then he is a bastard. Unwanted, unnamed. The Brotherhood named him Gabriel, after the Archangel, And eventually, He gave himself the Surname of Belmont due to his love of the mountains.
Once he became Dracula, He abandoned both his name and surname, and rechristened himself. (though so far he has only given us "Dracul" to work with, so we dont know if he gave himself a full name or what) Abandoning your name for a new one is a COMPLETELY different beast than giving yourself a name when you formerly had none.
For a new protagonist to give himself the surname Belmont, anything other than a direct family tie would just feel corny. And wouldnt even BE a Belmont by blood, but in name only.
*In b4 Gabriel is a Belmont in name only too* No he is not, since he is the first Belmont of this continuity. He took on the family name Belmont, and is thus the original Belmont. Where any future family got their name.