Is there another name for Mt. Sinai in the book of Exodus?

Mount Horeb, although there is some variance of opinion as to whether Mount Horeb is entirely synonymous with Mount Sinai or just a lower peak on the way up.

In certain biblical passages these events are described as having transpired at Horeb, but though there is a small body of opinion that Sinai and Horeb were different locations,[2]they are generally considered to have been different names for the same place.

According to the researchers of the Documentary hypothesis, the name Sinai is only used in the Torah by the Jahwist and Priestly Source, whereas Horeb is only used by the Elohist and Deuteronomist.[11]

See link 'Biblical Mount Sinai