In reply to henwardian:
Generally it's whoever establishes the route, which is open to interpretation.
For trad routes it's almost always the FA, except in rare cases where it's been someone's longstanding project with a name that ends up being 'given' to someone else.
For most sport routes in mainland Europe it's the equipper whose names are respected, with the quite rare exception of notably hard routes, as above, where the FA has something to say
For UK sport it's quite rare that the equipper isn't the same person as the FA, so the issue is moot, but I'd say the FA opinion would probably win if the two disagreed.