Did Peter ever actually wear the title pope?
The title pope (papa) was, as has been stated, at one time employed with far more latitude. In the East it has always been used to designate simple priests. In the Western Church, however, it seems from the beginning to have been restricted to bishops (Tertullian, On Modesty 13). It was apparently in the fourth century that it began to become a distinctive title of the Roman Pontiff. Pope Siricius (d. 398) seems so to use it (Ep. vi in P.L., XIII, 1164), and Ennodius of Pavia (d. 473) employs it still more clearly in this sense in a letter to Pope Symmachus (P.L., LXIII, 69). Yet as late as the seventh century St. Gall (d. 640) addresses Desiderius of Cahors as papa (P.L., LXXXVII, 265). **Gregory VII (1073 - 1085) finally prescribed that it should be confined to the successors of Peter. **
So . . .in answer to your question, “probably not”, at least not in the way we use it now.
Throughout the gospel and Acts, Peter was shown to be primary among the apostles.
The substance of the position of Bishop of Rome is there.
The earliest witness to Linus’s status as bishop was Irenaeus, who in about the year 180 wrote, "The blessed apostles, then, having founded and built up the Church, committed into the hands of Linus the office of the episcopate.
The word pope is from the Greek word for father.
The title *father *seems to have been commonly used in New Testament times when addressing or referring to older men, such as Peter.
And Stephen said: “Brethren and fathers, hear me…" (Acts 7:2)
And when he had given him leave, Paul, standing on the steps, motioned with his hand to the people; and when there was a great hush, he spoke to them in the Hebrew language, saying:“Brethren and fathers, hear the defense which I now make before you.” (Acts 21:40–22:1)
and saying, “Where is the promise of his coming? For ever since the fathers fell asleep, all things have continued as they were from the beginning of creation.” (2 Peter 3:4)
Our English word “Pope” is derived from the Italian word Papa which means “Father.” Since the English language as we know it did not exist at the time of Peter, he was not likely to have been called “Pope Peter.”
Might he have been called “father” in the language of the day? Possibly.
Not on his clothing, no.