I used to use a (female) nickname for anonymity sake on the internet sometimes and it kinda grew on me...
Since I liked both that nickname and by dead name somewhat, I decided that I'd try a mix between the 2 names and it sorta worked but I was never really convinced. That was until I was going through some old google accounts of mine and noticed that I had a profile pic of a character from a game that I really liked and was incredibly similar to the mix between my nick- and dead name (and could be considered gender neutral).
The only issue was: since it's a very uncommon name, not only did no one know how to spell it, there was also a very good chance that the responsible government agency for name changing stuff would outright reject the name because for some reason you can't have a uncommon/strange name (the rules are extremely vague).
So while that game char name grew on me for a year, I basically had to come up with the name that I actually took within like 2 weeks because of other regulatory issues...
So I picked a pretty common name where I can say "oh, please use [game char name] as a nickname". Don't get me wrong, I quite like the name I took but especially with friends/family it just feels way too serious in comparison. With most people even at work I go by the game char name as a nickname tho and I love it ( ᵔ▽ᵔ)
Edit: I also thought about using the female version of my former middle name - Valentina, but I have too many bad memories of getting made fun of my former middle name... Now that I think about it tho, I might add Valentina back as a middle name in the future