How interesting. I don't think I've ever used "my transgender" as in my gender, which is a trans kind of gender. I guess that could imply a "third"/"other"/nonbinary gender, or it could imply a man or woman gender done in a trans way (rather than a cis way). This is an ambiguity in all trans grammar.
When I was much much younger, I secretly wanted mythological names like Centaurs and Mermaids or something 😂😂 I never stumbled on a good metaphor that wasn't cutesy or appropriative or made any sense, and lots of people hate metaphor anyway, so never mind.