My understanding is there is a single payM database that has your phone number and designated sort code and account number associated with it.
Then when making a payment you are doing a lookup on this database with the phone number you are searching for and it pulls back the persons name to validate it’s the correct user (or advises the phone number is not registered). Then when you send the payment it goes the the associated account details for that number.
I think you can still send money to a number not registered and that number gets a text message saying there are funds waiting for them but they need to register. And the funds are returned if not claimed. Not 100% sure on this bit, could be wishful thinking on my part 
I suspect Monzo does something very similar with contacts but has implemented it in a much better way (you can see who is effectively registered for the service without having to guess by entering a number blindly). PayM could have done something similar but I imagine privacy concerns would have put a stop to it. 
I think banks need to embrace the ‘opt in’ model for privacy. For example; yes I don’t mind people knowing I have an account with Monzo, yes I don’t mind my transactions in push notifications, yes I don’t mind my balances being viewable without authentication, etc. And if people do mind then they don’t opt in. Simples 