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 the user interface to show that. In the HoloFuel app you will see unique identicons that are cryptographic icons based on the public key of each user.