I socially transitioned to using a different name, am gender-fluid, and I started about the same time as you. I don’t have my name officially changed on any card or anything, and I have a story that I use as to why I go by my current name instead of the one on my cards and documents. I also live in Japan.
How I socially transitioned (kinda long sorry)
I basically had all my friends (or at least the ones I trusted and also in online spaces) use my chosen name instead. I actually went through at least 5 names until I landed on the one that I did actually find myself responding to and liking. I also tried doing a Japanese name but only one friend called me it and it left a bad taste in my mouth so I stopped. I did this my last year of high school in the summer.
When I moved into a dorm in college, my RA was accepting and she remade my nametag which helped when I was introducing myself. I also emailed all of my professors ahead of time and got them on board with my name change and they were accepting as well, (some confused). Thankfully the following year my college changed its methods and had a spot to put preferred name and pronouns etc. From there on, there was no one who had called me by my “legal” name and the only people who looked at my card were bouncers and cashiers. They only ever asked my address or birth year if they wanted to check it. I got my family onto using it around 3 years of using it with my friends at school and also meeting new people who wouldn’t even assume the name I gave wasn’t “legally” mine.
Now that I’m in Japan, calling it a nickname has been helpful to avoid any dead name confusion, and any confusion gets stopped at a “well, this works for learning about foreign countries.” By this point, I have used my current preferred name for about 10+ years. While I was in the states, I did explain the pronouns etc, but since Japan doesn’t use many third-person pronouns and prefers to use someone’s name instead I’ve just kinda ignored it． plus I am not sure about the process now that I’m abroad the states have gotten more dangerous regarding laws etc about it. I’m afraid I’d have to go back in person to change it, but if I get married I’ll have to change my last name so what about both at the same time… hmmm 
..
I waited because I didn’t get my birth certificate from my mother until just before I was leaving for Japan. This didn’t give me enough time to start filing for a name change and now I’m (stuck) here.
All of this is to say that, please take care when changing your name. I personally think that a form of social name transition is a good way to see if you truly really enjoy the name you’ve chosen. Once I introduced myself as my name, I got different nicknames from it, I got different jokes made out of it, songs, and spellings as well. I wasn’t prepared for the new ways to, “make fun of” my new name until I experienced it. I also knew people who didn’t transition or anything, but their legal name from birth was something that could’ve been a giveaway of being trans. They were given a hard time and questioned to the point that they were annoyed by any question regarding their name whatsoever and wanted to change it to something more “normal/common” to avoid it. I even knew one used a nickname instead to avoid the situation completely. As a result, I’m glad I landed on something “common” and androgynous for my nationality and ethinicity.
But when you do know your name for sure, please change it legally. If I had known that I would settle on my current name and not change my mind, and if I had been able to change my name in addition to the birth cert being late and covid, my state used to require years of social transition plus therapist plus psychiatrist to allow a name change…I’m not sure what it is now, as I’m pretty sure it’s become illegal , I would’ve made it official. I felt confident in it when I was about 22/23. I’m 29 now and I really wish I had taken that plunge earlier.