The Hebrew word for father is very similar - אב (av or ab) - and in the Old Testament it's used only a few times to refer to God as our Father - usually when speaking of Him as our Creator and Protector. Isaiah in particular writes, "You, Lord are our Father," (Is 63: 16 and 64: 8) and Moses was the first to say it in Deut 32: 6. David says that God has a father's compassion and forgiveness towards His children. (Psalm 103: 12 - 13)
Solomon writes, in Proverbs 3: 12, that the Lord corrects those He loves, just as a father corrects a child he is pleased with. We tend to hold the stereotype that parents correct when they are displeased with us, but the proverb specifically says He corrects those He is pleased with; some translations even say a father corrects a child he delights in.
It's a really weak analogy, but I think I experienced this yesterday when I was teaching my dog a trick and filming it for our YouTube channel. The trick involved picking up rubbish and putting it into a pedal bin. Maiki got so enthusiastic that she kept leaping onto the pedal with both paws instead of just pressing the pedal with one paw. So I had to keep correcting her - not because I was annoyed with her, but because I was thrilled at how clever and how eager she was. Likewise, God corrects us because He sees our hearts, is pleased with us, and wants to help us do things better.- knows our needs and provides for us (Matt 6: 32 - 33)
- rewards us for our actions and attitudes (Matt 6: 1, 4, 6)
- forgives us (Matt 6: 14)
- gives good gifts (Matt 7: 11)
- gives us revelation so we can know Him (Matt 11: 26)
- answers prayer (Matt 18: 19)
- is merciful (Luke 6: 36)
- seeks true worshippers (John 4: 23)
- loves us (John 14: 23, John 16: 27)
- sends us the Holy Spirit (John 14: 26)
Of course, the New Testament is written in Greek, so many of those verses use the Greek Pater. But Jesus was an Aramaic speaker, so He was probably using the name Abba. When we read of His heartfelt prayer in the Garden of Gethsemane, Mark specifically tells us that Jesus prayed, "Abba, Father." Seemingly, Abba (אבא) was a more familiar form of Ab (אב) - more like Dad or Daddy.)
So, that's the name that Paul picks up when writing to the Romans and Galatians about our being adopted into God's family and given the Spirit that enables us to cry, Abba, Father. (Rom 8: 15, Gal 4: 6)
So, in this name we see a God who loves us, cares for us and provides us; who gives us good gifts and who corrects us so that we can become more like Him and be the very best version of ourselves.