✓ Banning someone from your service called "Dave"
Yep, it seems GDPR does not have any issue with your refusing someone "joining a service" based on some aspect of their personal information as long as it it not some discrimination related protected characteristic. So if you designed your system to not allow anyone called "Dave" you can do that.
✓ Banning someone changing their name to "Dave"
Surprisingly, despite the UK GDPR "right to rectification", a company, it seems, according to the ICO and even the parliamentary ombudsman, a company can refuse your changing personal information in any way they like as long as it is a "technical issue". I.e. if you designed a system that cannot handle some specific personal information for some arbitrary reason (such as a short email address, or a name of "Dave") then that is a valid excuse, even though nothing in UK GDPR seems to say it is a valid excuse, and you can refuse to allow the change.
Yep, it is all messed up. What a surprise!
P.S. changing your name to Dåve would probably be something you can insist on, due to case law: https://gdprhub.eu/index.php?title=Court_of_Appeal_of_Brussels_-_2019/AR/1006