Quite a few. The religious geography of the territory they conquered looked something like this:

Edge of Anatolia, modern-day Israel, and parts of Syria and today's Jordan-largely Greek Orthodox under the Patriarch of Antioch. These are the ancestors of the so-called "Melkite" churches.

Other areas of Anatolia and Syria, especially the upper Tigris: Largely Oriental Orthodox Syriac("West Syriac" more exactly), who rejected the council of Chalcedon(hence were "monophysite" along with the Copts) and who formed the ancestors of the Syriac Orthodox Church.

Southern Levant into northern Arabia-mixed, but the Ghassanid kings were very strongly Monophysite as well.

Iraq-under Persian rule, it was largely "East Syriac" (often called not very accurately Nestorian) under the Patriarch of Selucia-Ctesiphon. Salman the Persian would likely have been East Syriac or a convert therof.

Arabia proper-a mixture of Nestorian/East Syrians and Monophysites reflecting its position on the border between Rome and Persia as well as its proximity to Monophysite Ethiopia, which it had very close ties with.

This leaves out most details and many other important topics(please do ask follow-up questions!) but hopefully it will help situate you a bit.