Jehovah's Witnesses believe God is the Father whose name is the Hebrew YHVH, the Tetragrammaton, which was the name the Apostles called on to be saved.
However, after calling on the name to be saved, the New Testament states that those who believe and accept what has been done to restore the relationship between God and man should acknowledge they are sons of God by calling the Father "Abba:"
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]
And because you are sons, God has sent the Spirit of his Son into our hearts, crying, “Abba! Father!” (Galatians 4:6)
The term "Abba" is from the Aramaic אַבָּא vocative form, originally a term of endearment, later used as a title and personal name; rarely used in reference to God which is transliterated into Greek as ἀββα. It was taken over by Greek speaking Christians as a liturgical formula.
The use of "Abba" by the Greek speaking Christians is not surprising given Paul's instruction. Historically what is described with the name, is similar to animal sacrifice which those who rejected God's act of salvation believe is still necessary but the Apostles and all who believe understand are no longer required. In other words, where the Jewish people were told to call on the name of YHVH to be saved and to call on "the Father" (eg. in prayer) before the death and resurrection of Jesus, and still do, those who had been saved were to use "Abba."
Moreover, "Abba" is also how Jesus addressed His Father in the garden of Gethsemane:
And he 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)
How do Jehovah's Witnesses explain the requirement to use the name which was and still is associated with the Old Testament and its sacrificial system and not address God the Father in the way which acknowledges the current condition? In other words, since Paul says "Abba" is how someone who has been saved because the OT law has been fulfilled and is a child of God should address God the Father, how is instructing someone to use the Jewish name "Jehovah" consistent with the message of salvation Paul preached in the New Testament?
- Fredrick William Danker, A Greek-English Lexicon of the New Testament and Other Early Christian Literature, The University Chicago Press, 2000, p. 1