That would kill a lot of Twitter culture though (for better or worse). Changing a name for "spooky season", updating a profile pic to promote a new event, etc. It also would make it risky for a large company to change their logo (if Volvo loses verification for a few days it opens them up to a ton of scams).
Seems like a minor inconvenience compared to what's going on right now. Maybe allow changing avatar without losing the badge but not the name.
This is kind of how Scruff (gay dating app) works. Change your profile pic? Lose your verified status and have to go thru verification again.