I don't care how embarrassing it will be to your peers. If they ask you if you are dating someone, and you are in fact dating them, while they are standing right next to you, you fess up. In which case, one of two cases will occur:
1: The partner happily confirms it.
2: The partner desperately denies it.
Denying anything that is an actual fact will tell you a lot more of what that person thinks about you than you think. Heck, even discussing beforehand about hiding your relationship from your peers will tell you just as much. Hiding or denying anything means you are actually ashamed of it deep down, and that is going to hurt your partner deeply, turning your once positive relationship into a negative one, and that you would need to get out of there as soon as you can.