The overall feature is called “Send Money” or “P2P payments” in the Monzo world. Right now it’s just Monzo user to Monzo user but there was talk about PayM in the future. PayM requires an account number and sort code so it won’t happen until current accounts are launched sadly. Take a scroll through the sneak peak thread for some previous discussion on this.
https://community.monzo.com/t/sneak-peek-p2p-payments/55?u=richardr