Simple answer? Acts 20:28 and In the Greek The original Church of the New Testament was the "Church of God". The Catholic Church came along much later.
In John 17:11 Jesus prays to the Father right before his arrest that He (the Father) would protect them (The Apostles) by the power of His (The Father's) name. That's why the true Church was called "The Church of God".....and is duly called just that throughout the New Testament. It is never called the Catholic Church because, after all, that was not God's name! You will find the "Church of God" mentioned 12 times in the New Testament. You will never find the word Catholic mentioned. Check this Polycarp, Bishop of Smyrna, writing to The Phillipians about mid 2nd century. Very first line.
Actually St. Polycarp is how we got St. Ignatius' letters in the first place. In his letter to the Phillippians, he writes:
Both you and Ignatius wrote to me, that if any one went [from this] into Syria, he should carry your letter with him; which request I will attend to if I find a fitting opportunity, either personally, or through some other acting for me, that your desire may be fulfilled. The Epistles of Ignatius written by him to us, and all the rest [of his Epistles] which we have by us, we have sent to you, as you requested. They are subjoined to this Epistle, and by them ye may be greatly profited; for they treat of faith and patience, and all things that tend to edification in our Lord. Any more certain information you may have obtained respecting both Ignatius himself, and those that were with him, have the goodness to make known to us.
Your obsession with names is puzzling. Historically speaking, the "Catholic Church" and the "Church of God" are both used to designate the same entity, the congregation of the faithful who are subject to their lawful pastors, originally established by our Lord Jesus Christ through his Holy Apostles. The nominal use of the note "catholic," and the other notes of the Church, became necessary to discriminate between the true Church and the false churches of the heretics, but the Church is certainly considered by the apostolic record to be one, holy, catholic, and apostolic, just as is professed in the Symbol of Faith.
"What's in a name? that which we call a rose
By any other name would smell as sweet;"