It's absolutely not "wrong" to let people think you're gay. People will always assume things, it's just in human nature. However, if you're uncomfortable coming out to someone then you by no means have to. However, I would suggest not to say that you're gay, because this could make coming out later more difficult because if you say to them "I'm gay", then people may have you solidified in their minds as a gay girl rather than them thinking of you as gay, but not necessarily knowing.
Personally, I'm bi/panromantic heterograysexual. Lots of fancy words, but basically it means that I can be romantically attracted to anyone, and I'm mainly sexually attracted to women (but I don't experience a strong desire for sexual stuff, that's the "graysexual" part). I first came out as bisexual, but then I slipped more towards lesbian. Then a while ago I came out as nonbinary/androgynous, but now I've realized that I'm transgender.
So yeah, the labels really did progress really fluidly, it wasn't a very quick thing...
But honestly, I live in an accepting area and I go to a very accepting school, so I didn't really have to worry about being harassed because of my gender/sexuality (I was still terrified coming out as trans though... Still kinda am since I've only told close friends at school). Sorry I tend to rant and get off topic some times, but I guess the main point I'm trying to make is to do whatever feels best for you, not for other people. Only tell them what you want to tell them, and know that you're the only person who gets to dictate your life.