ETA: the last 2 posts weren’t there when I started.
I have zero relevant life experience other than once having some transitioning transexual grown-up employees. So here goes a shot in the dark worth every penny you paid for it …
Is there an opportunity to talk with him/her about what he/she thinks names mean? I understand and accept the idea of searching for identity. I question the logic that says identity is closely coupled to name.
Being a “Bob” is not really different from being a “Joe”. Being a “Linda” is not really different from being a “Catherine”. Changing ones name (within a single gender category) doesn’t change who you are or how it feels to be you. It’s not like Bobs are all cool and Joes are all dweebs.
If the kid is doing some autistic-typical thinking (AIUI), he could easily be placing the name cart well in front of the identity horse. IOW, he thinks that as his idea of identity morphs over time, that’s somehow proof the problem is his name, and if only he found the one that truly fits him, suddenly that name choice would cement the rest of his identity. Of course that’s poppycock, but it’s certainly the kind of thought process an autistic 13 yo could adopt. Everything MUST match.
Obviously as between an obviously male name versus an obviously female name there’s a divide there. Which can be fudged with one of the many mostly neutral names. Many, such as Madison, were male names until fairly recently and have since become mostly female. If he’s not sure which flavor he’ll settle on there’s lots of neutral-leaning-female choices to be had.
Bottom line:
Getting him to stop changing his name is not your goal. Your goal is to get him to stop *wanting *to change his name. Always work on fixing causes, not fixing symptoms. My bet is he doesn’t know why he wants to change names and you may be able to enlighten him that it’s pointless. Don’t push on how inconvenient it is to others or set limits. Instead work on the idea that adopting a new name is not doing anything useful to adopt a new identity.
Good luck.