This should've always been the case. If a verified person needs to change their name for some reason, they can get re-verified. There were problems with verified accounts impersonating famous people before Musk.
Or you could just prevent namespace collisions. Lots of people change their username for Halloween or other frivolous reasons; restricting everyone because of a mischievous or malicious few is a canonical example of inept rulership. Doubly so in this case, after Musk's recent grand declaration that 'comedy is now legal on Twitter.'
Merely enforcing "namespace collisions" implies you could still pretend to be anyone who isn't verified on Twitter. The concept of verification is itself a demonstration of a deeper problem with either Twitter or society, but if you are going to do it it has to mean something, and if you can change your name once you do it it doesn't mean anything anymore. If you want to change your name to something silly for frivolous reasons, here is a simple solution: don't expect to also be verified.
Surely you are aware that people on Twitter have a formal username (like @anigbrowl) and a more informal handle, such as 'Correct opinion haver', and that both are displayed simultaneously on every tweet. Changing one's handle is frequently done for comic effect; changing one's username (which is what people actually use to look others up) already auto-terminates verified status and has done for a long time.
If this is news to you then maybe you don't understand the issue as well as you thought. Self-styled 'chief twit' Musk instituted this policy preventing any name changes without notice (to the point that it's generating bug alerts in the mobile app instead of giving users an explanation) after rage-banning a comedian who changed their handle (but not their @username) to make fun of him.
Yes: I am well aware of this part of Twitter culture, as someone who has like half a million followers and a verified account on that platform. And yet, somehow, knowing a ton of people like doing it doesn't convince me that it makes any sense to allow it willy-nilly and in combination with this other feature, given the functionality of verification and the expectation that someone with a blue check next to their name is who they say they are.
The concept of being verified had meant that your display name and bio--not really your username, which could be a random string of characters; though, it was, of course, relevant--was a readable representation of who you are; so, if you can arbitrarily change that to anyone you want, it clearly doesn't do what it claims to do as people will see your new identity and your still-random username with a blue check. That changing your username would immediately lose your status and yet changing your display name and bio only does so if you abuse the privilege is non-sensical and somewhat ridiculous as it misses the entire point.
It also (but I already said this) seems fully reasonable to me that, if you want to be verified, you will simply not be able to take part in this mostly-silly and entirely-optional part of Twitter culture in exchange for having a blue badge that is supposed to ensure that people who see a username like "@MuscleNerd" knows it isn't Hank Green merely because they changed your display name to such. If you like dressing up in costumes, and you also think verified badges serve a purpose, it simply isn't unreasonable that you would need to have your costume verified to not look like someone else before into gets a blue check.
(Note: MuscleNerd isn't verified as he refuses to tell people his real name, so of course he can't do this, but I use him as an example because he is--or at least was, back years ago--both famous and has a glorious username that popped to my mind, as of course anyone working in science could have decided to go with "@MuscleNerd" as their username, so seeing the username by itself means nothing.)
Or, to be an asshole about it (as you were in your comment): "Surely, you realize that someone's username might have no correlation with their real name, and so the verification shouldn't have anything to do with the username and it's presence on a Tweet doesn't help prevent confusion. Hell: if people are expected to know someone is fake despite having a blue check just because their username is wrong, they clearly didn't need the blue checks in the first place as they already know the right username :/. If this is news to you then maybe you don't understand the issue as well as you thought."