God of all comfort is a New Testament name of God that includes the same Greek word that is often used for the Holy Spirit: paraklētos. One of the translations of that name is Comforter (KJV). The word literally refers to one who is called alongside to help and support. This name of God wonderfully expresses His care for us.
Some rabbis speculated that the first words of Isaiah 40:1 “Comfort, comfort, my people” were a hint that one name of the Messiah was Menakhem. Menakhem is a form of the word nekhamo (comfort). God certainly comforts people but there are no indications that it was taken as a messianic name by early Christians.
God of all comfort in Greek:
Theos pasēs paraklēseōs
Strong’s Concordance numbers: 2316, 3956, 3874
Bible reference: 2 Cor. 1:3
Blessed be the God and Father of our Lord Jesus Christ, the Father of mercies and God of all comfort, who comforts us in all our affliction so that we will be able to comfort those who are in any affliction with the comfort with which we ourselves are comforted by God. (2 Cor. 1:3-4)
When David pictured the Lord as a shepherd in Psalm 23, he told of His comfort:
Yea, though I walk through the valley of the shadow of death, I will fear no evil: for thou art with me; thy rod and thy staff they comfort me. (Ps. 23:4)
A similar phrase that includes the word paraklētos is Consolation of Israel. However, this is not likely to be one of the true names of God or the Lord Jesus (Yeshua‘).