Depends what you mean by limit but I'm choosing to interpret it as "exert undue influence over the choice of the parent". The UK's restrictions on names contain

Depends what you mean by limit but I'm choosing to interpret it as "exert undue influence over the choice of the parent". The UK's restrictions on names containing obscenities, numerals, misleading titles, or are impossible to pronounce seems reasonable although you could make arguments against all of those e.g. some words or names in other languages are obscenities in English and vice versa, numerals are traditionally used as a suffix to distinguish generations with the same name so why not be able to be Nathan3421, misleading titles is a bit stuffy and incongruous with existent names like Major, Judge, Prince, etc., impossible to pronounce already describes many names if you are not familiar with the native language. After all of that, I honestly don't think there is a good reason to restrict a name. Maybe the only limit I could think of would be to prove that it is given in good faith and not for some malevolent purpose.