Do you want to change the name from being Anonymous? If so, select the Edit and then change the name fields. If you clear the name field and don't put something into it, it will put Anonymous in.
If you want to delete the record, that is different because we don't delete records. It looks like it was created as a Barker for last name, so you could reuse it for a different person named Barker or merge it into another Barker record,