What are three different purposes of government?

The name श्रीमद्भगवद्गीता (Sreemad Bhagavad Gita) is derived from a combination of various words.

श्री (Sree) means wealth, prosperity, radiance, glory etc. So श्रीमद् (Sreemad) means “The one that is prosperous, radiant, glorious etc”.

भगवान् (Bhagavan) is a word used to represent the Almighty, God. भगवद् (Bhagavad) means “of the God, of the Almighty, etc”.

The word गीता (Gita) means “sacred song or poem”.

So Srimad Bhagavad Gita roughly means “The sacred song of the Almighty”.

If that troubles you, you can just call it Bhagavad Gita. There is no compulsion.