Ellicott's Commentary for English Readers
The principal variations are in Psalm 108:3, Jehovah for Adonai.
In Psalm 108:6 the construction is changed to suit the new arrangement and the variation in Psalm 108:10, on which see Note, Psalm 60:8. For the authorship of the parts of which the psalm is composed, see their Introductions. The ascription of the composite production to David furnishes a strong presumption against the historical value of the inscriptions.
A Song or Psalm of David. O God, my heart is fixed; I will sing and give praise, even with my glory.