To a Catholic: Was the first mention of the word "catholic" used to name the faith or to describe the faith?

A bit of both.

According to the four Gospels and the Acts of the Apostles, about the year 33 C.E., the structure of the Church was set up by Jesus Christ before His Ascension and then the early Christian Church was born on Pentecost when the Holy Spirit descended upon the Apostles and disciples.

This same Church has referred to itself as the “Catholic Church” at least since 107 C.E. (about 10 years after the last book of the New Testament was written), when the Greek term "Katholikos" (meaning universal) appears in the Letter of St. Ignatius of Antioch to the Smyrnaeans:

"Wherever the bishop appear, there let the multitude be; even as wherever Christ Jesus is, there is the Catholic Church."

http://www.earlychristianwritings.com/text/ignatiu...

We do not know how long they had been using the term "Catholic" before it was included in this rare surviving letter.

All of this was long before the Council of Nicea and the Nicene Creed from 325 C.E. which states, "We believe in one, holy, catholic, and apostolic Church."

http://www.newadvent.org/cathen/07644a.htm

With love in Christ.

The word "catholic" means "universal." The Catholic church adopted the name because the founders believed it to be the "universal" church.

Description by St. Ignatius of Antioch.

He called it the "Catholic Church," but it was a description, not a title... or an epithet if you will.

The bible mentions a number of churches. He didn't point to one of them as their mother. He, instead, pointed to Himself as their Father.