Well, as always, it depends on who's telling the story.
Generally, one's "true name" is the same thing as they were named at birth, if you're a real human in our world. There are exceptions though! And yes, one of those exceptions is trans people. However, in real world terms, if a person has never internalized their birth name for any reason, then their true name would be up for grabs, in that they could choose or otherwise a true name of their own.
Now, that is largely based on real world occult practices. But real world occult practices differ, sometimes significantly. There's some branches of ceremonial magic that hold the birth name you be the true name. Others that it's a chosen magical name that is never told to anyone, and a third "public" magical name is used for rites and rituals. So it isn't like there's only one way of thinking about this stuff in those belief systems.
But what about the fey/sidhe/fairies or other supernatural entities in fiction (and yes, there's a difference between literary fiction, mythology, and religious or spiritual beliefs in the real world. IDGAF if any given person wants to partake in those beliefs or not, they are different from fiction in several important ways that are off topic beyond saying that).
Well, that's when it comes down to the author/writer.
A lot of writers of things set in our world, even when it's a fictionalized version that works in a different way, tend to base their choices off of whatever mythology they've run across, then adapt that to their writing. So you run into a couple of different answers.
Mostly, they go with the birth name being the true name. There's exceptions, but it's the dominant trope. In some cases, the birth name isn't enough, it's the exact way a person says and thinks their name that makes it true. Iirc, that's part of the Dresden series if you want a specific example.
That idea is where words carry more than just definitions, and names are more than just some random phonemes. The process of how we (or the characters) take our name and etch it into ourself through thought and speech is what makes it a true name. It's a really neat idea tbh. Have you ever noticed that sometimes a mom or dad will say their kid's name slightly different? Minor changes in inflection or emphasis.
Plus, everyone sometimes says a name different. Your mom using your full name with stress in her voice hits harder than your friend introducing you to someone. And that's different from the DMV (or equivalent) person calling your name as next. The words are the same, but the energy is different.
So, the way we think of our name, inside, is ours in a way that nobody else can ever be exactly right unless we teach it to them. The way we speak it is different as well, but a supernatural entity in a story can overhear that part easy enough.
Which all means that there's no single answer to your question, but it's still a damn fun one :)