Early religious inscriptions mentioned God, but not Muhammed and used the term mu'minun rather than Muslim.
(There are early non-Islamic sources that mention Muhammed by name though, but not are aware that the Arabs are 'Muslim' they use Saracen, Hagarene, etc. for the best part of a century after being conquered by 'Muslims')
*copy/pasted from an earlier post*
Purely in terms of physical evidence, they called themselves believers (mu'minun). For example:
(It's Greek because Arabic wasn't adopted as the official language until Abd al-Malik's era)
- In the days of the servant of God Muʿāwiya (abdalla Maavia), the commander
- of the faithful (amēra almoumenēn) the hot baths of the
- people there were saved and rebuilt
- by ʿAbd Allāh son of Abū Hāshim (Abouasemou), the
- governor, on the fifth of the month of December,
- on the second day (of the week), in the 6th year of the indiction,
- in the year 726 of the colony, according to the Arabs (kata Arabas) the 42nd year,
- for the healing of the sick, under the care of Ioannes,
- the official of Gadara.
Interestingly, the person who made this inscription had time to carve a cross at the very beginning, but didn't see fit to carve Muhammed's name.
"But outside the Qurʾān, the word Islam, as a name of the religion, appears for the first time on the tombstone of a woman named ʿAbbāsa dated 71AH/ 691 CE.3 There, the Believers are called ahl al-islām. The first definitely datable evidence of the usage of the word muslimūn, in the sense of adherents of Islam, is from 123 Ah / 741 Ce,4 although it was prob- ably used widely even before that.5 Thus, the change from a “community of Believers to [a] community of Muslims”6 was a rather slow one, at least appellation- wise. Islam seems to have been a distinct religion from early on, but it took some decades, if not more, for its characteristics to become shaped."
(Muhājirūn as a Name for the First/ Seventh Century Muslims - Illka Lindstedt)