"So-and-so ibn So-and-so as-Salafi or Abu So-and-so as-Salafi" Should not be used
Attached is a question posed to ash-Shaikh al-Allaamah Muhammad Amaan al-Jaami' (rahimahullaah) regarding using the addition 'As-Salafi' or 'Al-Athari' after one's name, such as "Abu Fulaan Abdullaah ibn Abdur-Rahmaan as-Salafi al-Athari" (etc.) The Shaikh responds by saying that this was not the way of the Salaf, and it also implies self-praise and showing-off.
Rather what was common amongst the early Salaf was a connection to a location or a tribe, such as Imaam al-Bukhaaree, Hasan al-Basree, Ayoob as-Sakhtiyaanee, Abu Dawood as-Sijistaanee, An-Naisabooree, At-Tirmidhee, Abu Moosaa al-Ash'aree etc.