Coming from a Catholic person, I would say that hymns in Catholic mass could praise anyone from the trinity, just one of the people of the trinity (Father, Son, and/or the Holy Spirit), Mary Mother of God, the Pope, or any one of the hundreds of saints of the church.
If you're a Protestant Christian, then that really only leaves God and/or the trinity.
The English translation of the Te Deum is "We praise thee, oh God." The hymn is also called the Ambrosian hymn or A Song of the Church and it is an early Christian hymn of praise.
Gloria
The word you are looking for is "paean."
A homophone for "him" is "hymn," which is a religious song or a song of praise. These words sound the same but have different meanings and spellings.
a hymn of praise
A song of praise is called a hymn. Hymns are typically religious songs that are sung to show love, adoration, or devotion to a deity or higher power.
It refers to a religious song of praise, a hymn.
Song, usually denoting a hymn of praise.
song of praise, carol, chant, hymn, psalm, chorale, canticle
Acclamation, hymn, laud, ode, praise, psalm, song
It is called the "Te Deum Laudamus".
During the church service, the congregation sang a beautiful hymn that filled the sanctuary with reverence and praise.