They nor anybody else at that time called themselves "Catholic" or "catholic" simply because the word means widespread or universal. The absence of the word in your New Testament, therefore, is entirely attributable to the fact that the Christian church was in its infancy.
The combination "the Catholic Church" (he katholike ekklesia) is found for the first time in the letter of St. Ignatius to the Smyrnaeans, written about the year 110. The words run: "Wheresoever the bishop shall appear, there let the people be, even as where Jesus may be, there is the universal [katholike] Church."
The evangelists who wrote the Gospels are the foundation stones of the universal (or Catholic) Church.
I was told that Catholic is of the greek root kat-holike meaning “of the whole”. I thought that was interesting.
The catholic church is NOT the Catholic church...
It's ludicrous to suggest that God would allow a pagan emperor (Constantine) to be the 2nd head of His body, the universal church...