Majesty on high might have been a way of speaking of God without mentioning His personal name Yahweh (Jehovah). The Jews did not speak the name Yahweh because they did not want to mispronounce it or profane it in any way. They came up with several alternative names for God. In that sense, Majesty on high might be the equivalent of the name God on high. It is a name that tells of God’s exaltation.
Majesty on high in Greek:
Megalōsynē en hypsēlois
Strong’s Concordance number: 3172
Bible reference: Heb. 1:3
And He [Jesus] is the radiance of His glory and the exact representation of His nature, and upholds all things by the word of His power. When He had made purification of sins, He sat down at the right hand of the Majesty on high. (Hebrews 1:3)
Similar Greek names for God are Majesty in the heavens and Majestic Glory. One Old Testament name of God is Majestic One.