They do. I live in Germany where it is possible. Since 2022 (I think it was that year) we hsve a new law that makes it much easier. Before that, you had to undergo interviews with embarrassing and sexual questions that had nothing to do with a transgender identity (like "How do you m*sturbate" or "Are you dominant or submissive"). I'm grateful for the new law, but the reason I haven't changed my name yet is because I'm not completely sure. I'm pretty sure that my gender is non-binary (which exists as "divers"), but my current chosen name is still kind of an "experiment" (don't know how to say it). I feel extremely comfortable with it, but I might change it later. There's also some problems with having a non-binary gender in your passport, like coming out to everyone who sees your passport or having to get a special one in order to travel to countries that don't have this kind of gender available.
But I think just the fact that I feel extremely comfortable with my chosen name and my gender shows that I'm on the right path.
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