Charles Ellicott Commentary Psalms 68:15

"A mountain of God is the mountain of Bashan; A high mountain is the mountain of Bashan." — Psalms 68:15 (ASV)

The hill of God is ... — Better:

“Mountain of God, mount Basan;
Mountain of peaks, mount Basan.”

Even if the range of Hermon were not included, the basalt (basanite, probably from the locality) ranges, always rising up before the eyes of those looking eastward from Palestine, must have been doubly impressive due to their superior height and the contrast of their bold and rugged outlines with the monotonous rounded forms of the limestone hills of Judea. And it is quite possible that, in a poetic allusion, the term “mountains of Bashan” might include all the heights to the east of the Jordan, stretching southward as well as northward.

There would then be an additional fittingness in their introduction as jealously watching the march of Israel from Sinai to take possession of the promised land. Why these trans-Jordanic ranges should be called “mountains of God” has been much discussed. Some explain the term to denote ancient seats of religious worship; others take it simply as a general term expressing grandeur—“a ridge of god-like greatness.”