The name Sinai is probably related to Sin (wilderness of) and may even be an alternate spelling (cf. Exodus 16.1; 17.1; Numbers 33.11–12). Sin is one name of the ancient moon god that desert dwellers worshiped. The mountain is also called Horeb, mostly in Deuteronomy (see also 1 Kings 8.9; 19.8; 2 Chronicles 5.10; Psalm 106.19; Malachi 4.4).
Elwell, W. A., & Comfort, P. W. (2001). Tyndale Bible dictionary.
Picture: St. Catherine's Monastery @ the base of Mt.Sinai
Note: The worship of the Moon god " Sin" was widespread and common during the time of Abraham. Contrary to Muslim claims, Abraham was asked to leave Ur of the Chaldees where the moon god Sin was worshipped and migrate to Canaan and worship Jehovah. The Ur of Chaldees is in the region of Babylon. The names of the moon god in Arabia were Wadd, `Amm, Sin, Il Mukah, Hubal and Allah.