The name Elias has links and is likely to also be derived from the pagan Greek name Helios/Elios, spelt Ήλιος in Greek, and which literally means "sun".
It is known that the name existed for males in ancient Greece. At this time, the cult worshipping the sun God Helios was well established by all Greeks, despite being eventually replaced by Apollo. This implies the ancient name was derived from the god. Interestingly, there is evidence suggesting Helios was also worshipped by the ancient Jews.
After Christianity became the official religion of the Roman Empire, it is alleged that some pagan customs were incorporated into the new religion. This was to ensure an easy transition into the new religion by subjects of the empire, which included modern day Greece. Aspects of Helios's imagery were incorporated into the religion, as well as the name.
One telling piece of evidence is how in pagan times, the peaks of mountains were reserved for temples to Helios, the sun god. This was because it was the closest point to his presence. However in modern Greece, high peaks in many regions are named after Prophet Elias or προφητης Ηλιας. Alternatively one might view this as visible evidence of the new religion superseding the former, and asserting its dominance.
You touched many with your light. Shine on, my friend.
"Helios the sun-god became the prophet Elijah (the Greek form is Elias and, as the [...] had probably already fallen into disuse at the time of the changeover, the disguise was very thin). The name of this Hebrew prophet is now very common in Greece, but rare in Italy, where this name for Apollo was unknown. His shrine is always on mountains and hilltops where Helios, the heaven-born flaming charioteer, was worshipped. They symbolize, says the Church, Elijah's whirlwind assumption to heaven in a chariot of fire drawn by horses of fire; and hundreds of lofty peaks all over the Greek world still commemorate this personification of Apollo"