They never called each other Muslims until a couple of decades after the 1st fitnah (which looks very much like a civil war between Hijazi and Syrian factions). Back then they were still muminun (believers), which is the only designation that appears in any physical evidence. Muslim appears first at end of 7th C and then becomes ubiquitous very quickly.
Proto-Sunnis took another 50 years when Islamic Law started to be codified in Iraq.
Say (O Muhammad صلى الله عليه وسلم): "O people of the Scripture (Jews and Christians): Come to a word that is just between us and you, that we worship none but Allah (Alone), and that we associate no partners with Him, and that none of us shall take others as lords besides Allah . Then, if they turn away, say: "Bear witness that we are
Muslims." Qur'an 3:64
It makes sense for there to initially be believers, (Mu'minin) striving against the disbelieving Pagans of Arabia, but as the Message spread and people accepted it far and wide, the reverts were classed as Muslims as per the Qur'an's instructions.
Revisionist Historians have sought to completely ignore the Muslim narrative and tried to rewrite the History of Islam. Some are more qualified and measured in their approach than others;