When the Savior declares that He has made known the name of God the Father, it is the same as saying that He has shown the whole world His glory. How did He do this? By making Himself known through His wonderful works. The Father is glorified in the Son as in an image and type of His own form, for the beauty of the archetype is seen in its image. The only Son then has made Himself known, and He is in His essence wisdom and life, the creator of the universe; He is immortal and incorruptible, pure, blameless, merciful, holy, good. His Father is known to be like Him, since He could not be different in nature from His offspring. The Father’s glory is seen, as in an image and type of His own form, in the glory of the Son.
To call God “Father” is more exact than to call Him “God.” The word “God” signifies His dignity, but the word “Father” points to the distinctive attribute of his Person. If we say “God” we declare Him to be Lord of the universe. If we call him “Father” we show the way in which He is distinct as a Person, for we make known the fact that He has a Son. The Son himself gave God the name of Father, as being in some sense the more appropriate and truer appellation, when He said, not “I and God” but I and the Father are one, and also, with reference to Himself, On him has God the Father set his seal. And when He commanded His disciples to baptize all nations, He did not tell them to do this in the name of God, but expressly ordained that they were to do it in the name of the Father and of the Son and of the Holy Spirit.
St. Cyril of Alexandria