I believe possibly he chose to call Peter Cephas because he was identifying both the church and the person Peter who was jewish and Church.
One lesson might be. We, both as God's children and as members of the church should not disallow what God has allowed. Jesus would call him (fallible: Simon Peter) as (Peter: positionally correct and one of the 12 apostles, and (Cephas: Jewish and Church).
I could be wrong and can't wait to find out from the man himself. Hope this helps. :)
- Thou art Peter (ou ei Petrov). Christ responds to Peter's emphatic thou with another, equally emphatic. Peter says, "Thou art the Christ." Christ replies, "Thou art Peter." Petrov (Peter) is used as a proper name, but without losing its meaning as a common noun. The name was bestowed on Simon at his first interview with Jesus (John i. 42) under the form of its Aramaic equivalent, Cephas. In this passage attention is called, not to the giving of the name, but to its meaning. In classical Greek the word means a piece of rock, as in Homer, of Ajax throwing a stone at Hector ("Iliad," vii. 270), or of Patroclus grasping and hiding in his hand a jagged stone ("Iliad," xvi. 734).
On this rock (epi tauth th petra). The word is feminine, and mean a rock, as distinguished from a stone or a fragment of rock (petrov, above).
Used of a ledge of rocks or a rocky peak. In Homer ("Odyssey," ix. 243), the rock (petrhn) which Polyphemus places at the door of his cavern, is a mass which two-and-twenty wagons could not remove; and the rock which he hurled at the retreating ships of Ulysses, created by its fall a wave in the sea which drove the ships back toward the land ("Odyssey," ix. 484). The word refers neither to Christ as a rock, but to Peter himself, in a sense defined by his previous confession, and as enlightened by the "Father in Heaven."
The reference of petra to Christ is forced and unnatural. The obvious reference of the word is to Peter. The emphatic this naturally refers to the nearest antecedent; and besides, the metaphor is thus weakened, since Christ appears here, not as the foundation, but as the architect: "On this rock will I build." Again, Christ is the great foundation, the "chief corner-stone," but the New Testament writers recognize no impropriety in applying to the members of Christ's church certain terms which are applied to him. For instance, Peter himself (1 Pet. ii. 4), calls Christ a living stone, and, in ver. 5, addresses the church as living stones. In Apoc. xxi. 14, the names of the twelve apostles appear in the twelve foundation-stones of the heavenly city; and in Eph. ii. 20, it is said, "Ye are built upon the foundation of the apostles and prophets (i.e., laid by the apostles and prophets), Jesus Christ himself being the chief corner-stone."
Equally untenable is the explanation which refers petra to Simon's confession. Both the play upon the words and the natural reading of the passage are against it, and besides, it does not conform to the fact, since the church is built, not on confessions, but on confessors - living men. "The word petra," says Edersheim, "was used in the same sense in Rabbinic language. According to the Rabbins, when God was about to build his world, he could not rear it on the generation of Enos, nor on that of the flood, who brought destruction upon the world; but when he beheld that Abraham would arise in the future, he said: 'Behold, I have found a rock to build on it, and to found the world,' whence, also, Abraham is called a rock, as it is said: 'Look unto the rock whence ye are hewn.' The parallel between Abraham and Peter might be carried even further. If, from a misunderstanding of the Lord's promise to Peter, later Christian legend represented the apostle as sitting at the gate of heaven, Jewish legend represents Abraham as sitting at the gate of Gehenna, so as to prevent all who had the seal of circumcision from falling into its abyss" ("Life and Times of Jesus").
The reference to Simon himself is confirmed by the actual relation of Peter to the early church, to the Jewish portion of which he was a foundation-stone. See Acts, i. 15; ii. 14, 37; iii. 13; iv. 8; v. 15, 29; ix. 34, 40; x. 25, 26; Gal. i. 18.