“Hallelujah” (also sometimes rendered as "Alleluia") is another English transliteration of a word imported from another language.
In this case, the original word is from Hebrew, the language in which the majority of the Old Testament was written.
It means, “Praise Yah!”
“Yah” is the first syllable of the Name that God as identified as His own to Moses at the burning bush. Yahweh is I AM.
The ancient Hebrews and even many modern Jews today feel that God’s Name is too holy to be used in its entirety. Because their hesitation about using the full Name, they often said, “Hallelujah!,” meaning, “Praise Yahweh!”
The Name by which God has ultimately revealed Himself to the world is, “Father, Son, and Holy Spirit.”
As Luther writes in The Small Catechism, God gives us His Name so that we can use it to bring God, “prayer, praise, and thanksgiving.” All other uses are vain, meaning nothing, thereby disrespecting God and misusing the gift of God’s Name to us.
By the way, Jesus several times identifies Himself as Yahweh, as when He told His fellow Jews in a grammatically awkward phrase: “Very truly [Amen, amen!], I tell you, before Abraham was, I AM!” (John 8:58)