In the books of Tarajim, there are as-SÃlafee, as-Sulafee, as-Sil'fee, as-Salaqayy, as-Sailaqee, and of course, as-Salafee.
Al-Imaam adh-Dhahabi differentiated between all in his Siyar while talking about Abu Taahir, Ahmad b. Muhammad b. Ahmad as-Silafee whose grandfather had a heavy lip (silaf) and was thus referred to as as-Silafee. Many people do make mistake here concerning him whereby they refer to him as as-Salafee.
As-SÃlafee was a great scholar of hadeeth and fiqh of Persian origin. He was the Shaykhul Islam of his time. As-Sultaan Salahuddeen Al-Ayyoobi (who liberated Jerusalem from the Crusaders in his time, a story is coming on this Inshaa Allaah) was his student. As-Silafee died 576AH (1180CE) around 100 years of age. May Allaah bestow His mercy on him.
Al-Imaam Adh-Dhahabi however clearly stated it that whoever is upon the Aqeedah of the Salaf is a Salafee. He said Al-Imaam Abu Bakr as-Sarakhsee was one of them.
[As-Siyar 15/265, Daar al-Ghad al-Jadeed Edition (2021), with additions.]