This chat app doesn’t have any restrictions on usernames, and doesn’t enforce unique names. You could build that into an app if you need it.
In Holochain, it is virtually impossible to actually impersonate another user because every action and communication you make is signed by your private key. However, in Elemental Chat we haven't designed usernames that reflect that fact. User avatars, on the other hand, are unique, unforgeable 'identicons' that are generated directly from the user's public key. We will also use these in the HoloFuel app to protect against fraud.