What do Catholic traditions say was the real name of St. Thomas?
Saint Thomas the Apostle (also known as Judas Thomas or Didymus, meaning "Twin") was one of the Twelve Apostles of Jesus who is best known for doubting the resurrection of Jesus and demanding to feel Jesus' wounds before being convinced (John 20:24-29). This story is the origin of the term "Doubting Thomas."
I have heard of Catholic tradition that suggests that St. Thomas was the twin brother was the twin brother of Judas Iscariot, but I am unable to locate a source to reference for you. I would explain why St. Thomas was such a doubter! This almost makes sense as we do not know who is his twin!
Contrary to what you state the Gospels do mention his real name: Thomas. The etymology of his name shows that if he had a nickname it would have been Didymus meaning twin and not Thomas.
The name Thomas is derived from the Aramaic personal name תאומא /tɑʔwmɑʔ/, meaning "twin," and the English spelling "Thomas" is a transliteration of the approximate Greek transliteration, Θωμάς. Thomas is recorded in the Greek New Testament as the name of Thomas the Apostle (one of the twelve apostles of Jesus). - Thomas (name)
With Didymus and Thomas both meaning "twin," the real name here is Judas Thomas.
This equally seen in the Catholic Encyclopedia:
Little is recorded of St. Thomas the Apostle, nevertheless thanks to the fourth Gospel his personality is clearer to us than that of some others of the Twelve. His name occurs in all the lists of the Synoptists (Matthew 10:3; Mark 3:18; Luke 6, cf. Acts 1:13), but in St. John he plays a distinctive part. First, when Jesus announced His intention of returning to Judea to visit Lazarus, "Thomas" who is called Didymus [the twin], said to his fellow disciples: "Let us also go, that we may die with him" (John 11:16).
There are also certain historical data which suggest that some of this apocryphal material may contains germs of truth. The principal document concerning him is the "Acta Thomae", preserved to us with some variations both in Greek and in Syriac, and bearing unmistakeable signs of its Gnostic origin. It may indeed be the work of Bardesanes himself. - St. Thomas the Apostle
The Acts of Thomas identifies Judas as the Apostle Thomas. The evangelist, John, also identified Thomas as "the twin."
Saint Thomas the Apostle is equally known as:
- Apostle of India
- Doubting Thomas
- Judas Thomas
- the Twin