I'm currently using Twilio Frontline on top of my conversation service and my identity for each user is a uuid so when a message comes in on Frontline, it displays that user's uuid. This can get confusing if we have multiple participants in chat. Assigning a name as the identity would not work since it may not be unique. Assigning their email as the identity would not work as well if they update the email.
In Conversations, the name of a participant in a conversation comes from the underlying User resource and the FriendlyName property.
You can update Conversations Users using their identity as the key in the URL and set the FriendlyName, that will then show in Frontline instead of the identity.
We also recommend using the onParticipantAdded Conversations webhook to do things like setting a customer_id, avatar and display_name for customers in a conversation.
You can read more in the How to enable incoming messages? section of our Quickstart Guide.