PeerID is available as an expression in certain triggered multiplayer conditions like on peer connected and on message received. When used in those triggered events, it will give you the ID of the relevant peer.
Normally you would store this in an instance variable in an object associated to that peer upon them connecting, but you can use any data structure you want, like a dictionary (key:value=name:PeerID) or an array.
In the case of a chatroom, the simplest way would use a text object with an instance variable. Upon joining, set the text object to display the name of the user, and save the PeerID to an instance variable in that text object. Then for example if you clicked that name, it would be easy to get the associated PeerID.
I would probably use a dictionary myself for flexibility, but that is a slight bit more complicated.
Edit: You'll learn how to get and use PeerID better in the fourth multiplayer tutorial. That's why I'd recommended following and understanding all the multiplayer tutorials before using the multiplayer plugin, even if your end goal is just a chat room. The multiplayer plugin and multiplayer concepts are very complicated, so cutting corners will often lead to frustration in the future. The tutorials seem long, but they're actually quite concise and thorough.