I don’t know of any sources contemporary with the invasion itself, but the general term used in Asia from pre-Hellenistic to modern times to refer to both the Greeks proper and to the Macedonian successor-states was “Ionian” (or words derived from it—like “Yauna” in Persian, “Yavana” in Sanskrit, and “Yavan” in Hebrew).

Ionia was the Greek-speaking region on the Aegean coast of modern Turkey that was subject to the Persian Empire; the Ionians therefore traveled widely throughout the empire and became known as far as India. So “Ionian” became the common term for all Greek-speakers, and was used throughout the east to refer to Alexander and his successors in the Hellenistic era.