Why did Jesus never address God by the name "Jehovah"? What explanations have been offered for why Jesus never addressed God in His prayers by the name "Jehovah" or "Yahweh"?
The word Jehovah is a Latin version of the Tetragrammaton, usually considered the Hebrew name of God. Most scholars consider Jehovah "a hybrid form derived by combining the Latin letters JHVH with the vowels of Adonai", and not to have been used before 1100AD. Obviously Jesus would not have used a word invented 1100 years after his earthly life.

It is widely thought that Jesus DID use the Hebrew name of God, in John 8:58:


  “Very truly I tell you,” Jesus answered, “before Abraham was born, I am!”


The reaction of the hearers was such that they clearly believed he was using the name of God.

It was the practice of the Jews not to use the name of God at that time, so he may simply have wished to not muddy the waters by giving offence. Technically the name YHWH applies just as much to him as it does the Father, so that may have accounted for it.