Christians Calling Themselves Catholic

In the early second century about 110 AD 80 after Jesus’ death we have a letter by St. Ignatius of Antioch to the Smyrneans calling themselves Catholic. Here is an excerpt

“Chapter 8. Let nothing be done without the bishop

See that you all follow the bishop, even as Jesus Christ does the Father, and the presbytery as you would the apostles; and reverence the deacons, as being the institution of God. Let no man do anything connected with the Church without the bishop. Let that be deemed a proper Eucharist, which is [administered] either by the bishop, or by one to whom he has entrusted it. Wherever the bishop shall appear, there let the multitude [of the people] also be; even as, wherever Jesus Christ is, there is the Catholic Church. It is not lawful without the bishop either to baptize or to celebrate a love-feast; but whatsoever he shall approve of, that is also pleasing to God, so that everything that is done may be secure and valid. ”

and the source.