How do I talk about my identity on a date?
Say the short version, then change the subject. You are on a date, not at a hearing.
The trap is letting it become the topic. Once the conversation is about your gender it stays there all evening, and you go home having explained yourself for three hours instead of finding out whether you like this person.
Have a short version ready
One or two sentences, said calmly, that you have actually said out loud before. Not a speech. Something like: I'm trans, I've been out for a few years, it's not really the headline for me — and then a question about them.
The point of preparing it is not performance. It is that you get to decide the framing instead of improvising while someone stares at you.
Then move
Ask them something immediately after. Anything. It signals that this was information rather than an invitation to interview you, and most people follow that lead without noticing they were led.
If they want to sit in it and ask twenty things, you can say: I'm happy to talk about it another time, but I'd rather hear about your week. That is polite, clear, and it works.
You choose the depth
There is a difference between a question that is about you and a question that is about the category. "What was it like telling your family?" is about you. Questions about your body are not, on a first date, about you either.
You can answer some and not others without justifying the split. "I don't talk about that with people I've just met" needs no follow-up, and someone reasonable will take it and move on.
If they get it wrong
Someone who uses the wrong word once and corrects themselves is fine — let it go, and note that they corrected it. Someone who keeps doing it after being told has told you something about how much attention they are paying. That is worth more than any apology.
The word for it is misgendering, and you do not have to manage their embarrassment about it. A brief "it's she" and carrying on is enough.
Names and history
Your name is your name. Nobody is entitled to a previous one, and "what was your name before?" is a question you can simply decline. The term for the old one is a deadname and it is not small talk.
What a good sign looks like
They take the short version, respond like a person, and return to the conversation you were having. Later they use your pronouns without ceremony. Nothing about the evening is organised around it.
That is the whole bar, and it is met more often than the internet suggests.