“The name ‘Father’ is now the common name of God in the New Testament. The name YHWH is inadequately conveyed by Lord (κυριος) and is, as it were, supplemented by the name ‘Father.’
This name is the supreme revelation of God. God is not only the Creator, the Almighty, the Faithful One, the King and Lord; He is also the Father of His people.
The theocratic kingdom known in Israel passes into a kingdom of the Father who is in heaven. Its subjects are at the same time children; its citizens are members of the family.
Both law and love, the state and the family, are completely realized in the New Testament relation of God to His people. Here we find perfect kingship, for here is a king who is simultaneously a Father who does not subdue His subjects by force but who Himself creates and preserves His subjects.
As children, they are born of Him; they bear His image; they are His family. According to the New Testament, this relation has been made possible by Christ, who is the true, only-begotten, and beloved Son of the Father.
And believers obtain adoption as children and also become conscious of it by the agency of the Holy Spirit (John 3:5, 8; Rom. 8:15f.). God has most abundantly revealed Himself in the name ‘Father, Son, and Holy Spirit.’
The fullness that from the beginning inhered in the name Elohim has gradually unfolded and become most fully and splendidly manifest in the trinitarian name of God.”
–Herman Bavinck, Ed. John Bolt and trans. John Vriend, Reformed Dogmatics, Volume 2: God and Creation (Grand Rapids, MI: Baker Academic, 2004), 2: 147.