I’m sorry, but God is not our “daddy”!
To call the Almighty God “Daddy” is misguided at best, and disrespectful (in Biblical terms, profane) at worst!
I have never believed the claim that “Abba” is a term of childish endearment reserved for New Testament Christians. Going back to prophetic times or farther, it has been common for orthodox Jews of all ages, to refer to their parents as Abba and Eema. It is simply a respectful term for “father”, or the more Middle Eastern form, “my father.”
The word, Abba, is found three times in the ESV New Testament:
[36] And he [Jesus, in the Garden of Gethsemane] said, “Abba, Father, all things are possible for you. Remove this cup from me. Yet not what I will, but what you will.”
—Mark 14:36 (ESV)
[15] For you did not receive the spirit of slavery to fall back into fear, but you have received the Spirit of adoption as sons, by whom we cry, “Abba! Father!”
—Romans 8:15 (ESV)
[6] And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!”
—Galatians 4:6 (ESV)
So, what is the significance of this twofold representation, if both words are equivalent? Abba was originally an Aramaic term, which was “borrowed” by Hebrew. It is the respectful way the children in Israel would have addressed their fathers. I believe that the Greek language of the 1st century Scriptures was simply repeating it the way it was spoken by Jews, and then translating it into Greek for those not understanding it.
By the way, an Old Testament example of the same term, used by Jews long before the incarnation, is found in:
3 And I went to the prophetess, and she conceived and bore a son. Then the LORD said to me, “Call his name Maher-shalal-hash-baz; 4 for before the boy knows how to cry ‘My father’ [אָבִ֣י, ’ă·ḇî, ‘aba’ with syntax, one of 196 occurrences] or ‘My mother,’ [וְאִמִּ֑י, ’im·mî, ‘eema’ with syntax, one of 23 occurrences] the wealth of Damascus and the spoil of Samaria will be carried away before the king of Assyria.”
— Isaiah 8:3-4 (ESV)
The Back of My Mind 