When did the Church become known as Catholic?
Although the name Catholic is not applied to the Church in the Bible, Christ and the apostles had the concept of catholic in mind, as catholic comes from a Greek word meaning universal. The Catholic Church is certainly universal; that is, for all people.
Notice that St. Ignatius did not write of the Catholic Church as if he were giving it a new name, but rather as though the name had long been in use. It is reasonably safe to assume, then, that the Church was probably called Catholic during the latter part of the first century. Indeed, it is likely that St. John the Apostle had heard the Church called by the name Catholic, since he died around the year A.D. 100.
"Where the Bishop is, there let the multitude of believers be; even as where Jesus Christ is, there is the Catholic Church" (Ad Smear., 8:2).