What does: "What is your trademark?" mean?

In this case, I think they mean “What are you well known for?”

Yes, It’s if someone asked your friends what’s the first thing that pops into your mind when someone says Christina.

Must… not… be… snide… aaaaashgsahghnnnblaaaaargh…...

Trademark, you know, like a tramp stamp – the mark of one’s trade, what one is known for, and so on xD

Your speciality, mostly relating to what you can do.

I would guess it could be a thing, or also a phrase. Something you have or wear or do or say that makes people think of you immediately, instead of any other student. In business, a trademark is anything that reminds you of a specific product, and distinguishes that product from other similar products in your mind.

A characteristic saying, perhaps? Or something you wear a lot. Something you always do. Something that you are always being teased about?

Yes, what @burntbonez said.
I have been told my “trademark” or “signature” is my hair, pigtails done up with sparkley, beaded, bracelets for ties. Your “trademark” can be anything that is unique to your self expression.

Indiana Jones has his hat. The Jedi his lightsaber. Hemingway has alcohol. That sort of thing.