Mt 16:18 specifically says Simon was given the name (title) “Peter” by Jesus.
Matthew 16:17-18 -- “And Jesus said to him, ‘Blessed are you, Simon Barjona, ... I also say to you that you are Peter [Πέτρος; rock], and upon this rock I will build My church;”
Like the word “refrigerator”, neither the words Cephas nor Peter were personal names at that time. This is relevant because two leading figures of early Christianity could not be rationally given the same obscure nickname when nicknames served precisely to distinguish persons in such contexts.
• Bart Ehrman: “Peter is the Greek word for ‘rock,' which in Aramaic was Cephas. And so Jesus gave this person—his real name was Simon—a nickname, ‘the Rock.’ It seems highly unlikely that two different persons were given precisely the same nickname at the same time in history when this name did not previously exist.”
Both Simon (Peter) and Cephas share properties.
• They both share the highly unusual nickname “rock” (see above).
• They are both the first male witness. (1 Cor 15:5; Lk 24:34)
• They are both identified as a prominent apostle (if not the most prominent).
Peter and Cephas are never located together in any way. This is relevant because, given their prominence, we could expect them to appear together by chance at least some times. In general what we know about both fits perfectly with their being the same individual, which is highly unlikely to be a coincidence.
It says in 1 Corinthians 15:5 -- “[Jesus] appeared to Cephas, then to the twelve”. This is relevant because this arguably distinguishes Cephas from the twelve.1
By way of response, however, the creed seems to straightforwardly match the gospel report that Jesus appeared to Peter first (Lk 24:34), then subsequently to the apostles as a whole, which obviously does not exclude Peter from being among them (Lk 24:36-49).2
“saying, ‘The Lord has really risen and has appeared to Simon.’… While they were telling these things, He Himself [Jesus] stood in their [the apostles] midst and said to them, ‘Peace be to you.’” The sequential nature of the 1 Cor 15 creed is evident enough from how the four events are presented in sequential order (death, burial, resurrection, appearance), and how the rest of the events in the list are consistently accompanied by further sequence indicators like “then”, "after that", and “last of all”. Here is the text: “He was buried, and that He was raised on the third day according to the Scriptures, and that He appeared to Cephas, then to the twelve. After that He appeared to more than five hundred brethren at one time, most of whom remain until now, but some have fallen asleep; then He appeared to James, then to all the apostles; and last of all, as to one untimely born, He appeared to me also.” A better argument would have been from 1 Cor 9:5 “Do we not have a right to take along a believing wife, even as the rest of the apostles and the brothers of the Lord and Cephas?”, but this hardly implies Cephas was not among the “rest of the apostles” any more than does “Go tell the disciples and Peter…” (Mk 16:7).
Paul never explicitly says Cephas is Peter. This is relevant because presumably, Paul would have said so explicitly.1
But so what? Couldn't it simply be that there's no reason to think they would have to be explicitly equated in the works we have?2