In addition to what has already been noted, I’ve seen scholars also point out several historical issues that likely attended naming Pilate in the Creed.
1) It reinforces the historicity of the Passion, as the governorship of Pontius Pilate is attested by several non-Christian sources, so naming him is a reminder of sorts that Jesus’ death factually occurred within the context of Roman rule and at a specific time in human history.
2) The three main charges brought against Jesus by the Jews were of a largely political nature. “We have found this man… perverting our nation, and forbidding the payment of taxes to Caesar and saying that he is Christ the king” (Luke 23:2) So to name the most relevant political figure involved in the matter makes sense.
3) I find this suggestion most fascinating of all… There is some debate over its date of origin, but it is thought that by the 2nd Century a proto-gnostic writing known as The Acts of Pilate (aka the Gospel of Nicodemus) was in circulation. This writing included a number of fake letters by Pilate, which portray him as a convert. The acceptance of this almost certainly false notion was even alluded to by Tertullian, who described Pilate as someone “who himself also in his own conscience was now a Christian.” (Apology, 21) The Acts further alleged that the emperor Tiberius was so convinced by reports from Pilate that he made an unsuccessful effort to have Jesus placed among the pantheon of Roman gods. There seems to have been several variations of the Acts, and its influence is particularly seen in the early 4th century - the same time the Nicene Creed was created - when an anti-Christian, pagan version was created in an attempt to discredit the supposed “Christian” account. So a reiteration of the biblical emphasis of the fact that Jesus suffered under Pilate would serve as a counterbalance to the ongoing deceptive use of his name, and the fallacious ideas that flowed from it.
