I don\'t know about Europe. In the US, three situations happen:
1) A potential problem names as \"Project\" when it is still not climbed either by TR or by any other ways. Soon as TRed, that is, soon as the problem proved to be climbable, this route is named (if memory serves me right, both \"To Bolt Or Not To Be\" and \"Just Do It\" belong to this type of naming history, among many others)
2) A \"Project\" remains as a \"Project\" until it is bolted, leading-climbed, and so named (this seems to be what is being argued here -- leading-climbers, not otherwise, have the \"rights to name\".)
3) An existing route changes by either variation (a section, or sections, of it goes to other ways but begins and ends at the same points) or by adding length to it, so the difficulty is changed. In this situation, either a \"Variation\" would be added to the old name of this route or a new name would be given to indicate the new difficulty with those variation(s).
In any event, it is rare to re-name a route if the name of that route (no matter this was done by leading-climbers or TRers) has already existed. Doing so would be thought as being self-grandizing and often local people would simply ignore it.
In short, in terms of naming, it is common for the one who has \"discovered,\" \"attempted,\" and \"cultivated\" the potential of a route to do so, not necessarily the one who \"finishes\" it. If one argues for the latter, then, the question would be extended to this next question: by what standards -- on-sight, flash, red-point, pink-point, or some other even fussier differentiations? If the \"rights to name\" is the point argued here, then I would say that one who has on-sighted a named route should have the \"rights\" to rename it because its name was done by one who simply red-pointed it, and so forth. The \"strength\" is the foundation of the \"rights,\" so it goes, and if I am stronger than you are, screw your rights, and screw your name.
Is this what Taiwan wants? I hope not. If you can do 5.13b, regardless whatever its name and regardless whoever has the \"naming rights,\" you can do 5.13b, and that is all about for proving and inspiration. When Lin Hill came to Lander, Wyoming, and on-sighted a 5.13b route at Killer Cave (Two-teeth and Min-Che were there 3 years ago), which route\'s name was given by a guy who did it only by repeatedly hangdogging, Lin did not change the name of that route. Why should she?
A name, and relatedly, the \"rights of naming\", is for the purpose of identification, to indicate a problem or challenge that lies there to be overcome and having fun. Naming is just a way for communication, to simply put. To argue for \"naming rights\" is misleading, and kinda of funny -- years later, people would only remember who did that 5.13b or 5.14a and the same people would hardly remeber who named those routes. Who care?