If I *had* to pick a new name for myself now, as in the thing the Government calls me, I don't know what I'd pick.
There's the trope I mentioned about trans names - there are also a bunch of stereotypical names for Chinese nationals in the US to pick.
See: every Vivian I've ever known.
I've been out for 10+ years and I still don't know what I would pick - I go by "Gee" or G, the initial of my assigned first and middle names. My parents really thought they were cooking giving us all old lady names with double initials. 🙄