

This is already location-dependent. I think Iceland has the most restrictive legislation with a prescribed list to choose from. Other countries have a layer of “is this really a name?” checking as part of the registration process after birth and parents can be sent back to square one.
I think there is a balance to be had where you can’t get away with xc1>df or whatever but you could name your kid after a GoT character that tragically turned evil in the last season. My suggestion would be to include a second given name that is more established than Khalisi or Dumbledore, e.g. Kelly and David. If Khalisi Kelly’s last name is Knox obvs I wouldn’t insist on the alliteration. My point is then your child has a plan B when they get mocked for being called Hobbit in school. They can just go by Henry or whatever other boring name made the cut. That way you don’t need to get into a complicated legal situation where a minor would have to override the wish of their parents.
After reaching adulthood legally, virtually anybody can try to change their name. Although the process may involve having to prove harm to get it approved in some places. I think there is a correlation between a laissez-faire attitude to naming and ease of getting a name change. In countries that are stricter to begin with, the hurdles are much higher and can be much costlier.
Technically, they don’t have to be. They could elect a venerable whippersnapper cardinal - Dan Brown wrote a book about that. And that tells you how likely that is if he wrote the story. But it is possible.
It would be rare because it takes seniority to get into the position. And politics to be well liked enough to be put forward and then elected. By mostly old people. Some of whom would like the job themselves.