how do i change youtube username properly?

if the channel is verified, changing the name removes the tick and you have to apply for it again. there's also a cap on how many times you can change it in a short window, so settle on the name first and change it once.

handle and channel name are two different things. studio, customisation, basic info for the display name. the @handle is changed separately, and your old one goes back in the pool when you do.