RE: Are you Shiftkin?
I personally prefer the term "polymorph", just as Blu McCaw used above. That's at least what I've always heard what the op is describing being called. I have, however, also heard it called, "shapeshifter". While both terms can be used interchangeably, I would think "polymorph" would be clearer, given that "shapeshifter" could potentially be confused for claims of p-shifting. It's just the way I see the words, of course...
Nevertheless, the op makes good points. I actually had a lot of difficulty finding my theriotype as well, and my difficulty was due to a number of reasons. For one, my theriotype is extinct and lesser-known, and I was a bit afraid of identifying as something extinct. Another reason was community trauma early on. An admin of one site essentially was abusive toward me, and I spiraled into an identity crisis for years after that. I think another thing that doesn't help a lot of therians (that happened to me as well early on) was when people would pretend they knew my theriotype, when in fact, they did not. While I do believe in psychic ability, I've also noticed that a lot of people who are not psychic in the community, claim to be...but only outside of the spotlight, and behind the scenes. I'm not sure if they do this for their own superiority or to manipulate, but it definitely is something that happens.
So another reason behind the difficulty faced by those having trouble pinning down their theritoype could be negative community influence, I suppose.