When registering a new account, there should be a field to fill in your name (maybe it should even be pre-filled with your real name from your user account information). Currently, one has to press "Edit Identity" on the new account to set it. Reproducible: Always
Can we actually do that? I mean backend-wise?
Yes.
Dear user, unfortunately Telepathy is no longer maintained. Please migrate to another solution, e.g. for Jabber a possibility is Kaidan, for Matrix a candidate is NeoChat.