I'm happy to be proven wrong, but my understanding has always been that you have to pick and choose.
That said, there's nothing stopping your PC from claiming noble heritage, even if it happens to be in a form that wouldn't be readily recognised in the various mechanical ways that the reward is on the server. I've certainly done this, and had a fey'ri claiming noble descent from a house so long dead that anything that would translate to meaningful mechanical benefit is gone.
If you're from a particularly uncommon / exotic race, you could reasonably imagine that the average person isn't going to recognise your particular iconography or history anyway. Or, at least, certainly not in the way they would Lord ABC from Waterdeep.