Well, if you plan to play together for any length of time, I think that whatever name you finally chose should have some meaning for you. (Do you really want us to pull a name out of the air?)
You could name your trio after where you live. (e.g. Hoboken Trio, not saying that's where you're from.)
Your favorite composer. (e.g. Amadeus Trio, though there already is a quartet with that name.)
Of course, you can look at all kinds of musical terms. (Andante, allegro, col legno, although the Con Brio Trio is just a little too nursery-rhyme-y.)
You could name yourselves after a favorite teacher or a role model.
An astrological sign. (When did you decide to play together, when was the trio "born"?)
I could go on and on and I'm sure you will get some very interesting suggestions from members of this forum. (Pianistimo

)
Anyhow, best wishes and good luck in your new endeavor.