Hello! Please, I have the free version of Avast! and I’m puzzled to have found a mysterious username next to mine (I know nothing about!) Could someone give me a hint of what is this about? Thank you! [Check attached pic]
That’s your karma points, not a user name.
Certain things you do within avast earn you points 
I would advise you to either edit your email from that picture or remove the picture.
In addition to what Craig has said, here is more information about karma points/badges etc.
https://forum.avast.com/index.php?topic=160021.0