Pretty certain that when you go through the pairing process on the 810 (and presume the 510 also) it does so within the context of the selected bike. Do you have multiple bikes set up on your 510?
Edit: don’t have my 810 with me but looking at the manual seems to confirm that you should be selecting a bike profile, then pairing a sensor. The sensor ID would then be tied to that bike profile.
Double edit: having re-read the post, do you mean that when you initially try and pair with, say, a new cadence sensor, if there are multiple ones then is there a way for you to select which one? I don’t think this is possible. You would need to isolate it and then pair it… but once it’s paired it should then only try and find that one next time you turn it on.