Hi, I'm making a similar game, I realized working with multiplayer stuff is much easier than I initially thought. And yes, this was the very first challenge: Send your name to host/peer, and retrieve his/her name.
This can be done through "Send Message" option of Multiplayer, and likewise, "On Message received"... In fact, my whole multiplayer game uses only Sending and Receiving messages to communicate, and it works perfectly! (i.e. as long as it is a turn-based game)
So, let's say, when you type your name, On button pressed, you can choose > Multiplayer > Send Message
(this will be done in common, right? whether it is the host or peer), so you need to include a sub event there:
if host > Send Message (to Multiplayer.peerID, tag: "name", message: name.Text or whichever)
else > Send Message (to Multiplayer.HostID, tag: "name", message: name.Text or whichever)
Then, in the Host Group only, have a condition:
On receive message "name" > Set oppname to Multiplayer.message
And likewise, in Peer Group, have similar condition:
On receive message: "name" > Set oppname to Multiplayer.message
If you can do this, you can communicate anything from peer <--> host by just sending "messages" with information, throughout your game.
Let me know if this helped.