The name Catholic Church has been around since even before the time of Saint Augustine. It was an old name even by than. So the official name of the Church did not start in the Great Schism as some like to think.
Also, the dispute between the Orthodox and Catholic Church is rather interesting, name-wise, because some people think that there were no conflicts in the Church before the Great Schism. Yet it is evident from the Epistle to Timothy that the Church was plagued with false teachers and heresies ever since her humble beginnings. So I think the Church’s official name came early on to distinguish her from other churches and to show what she was: the Catholic Church.
And now to back up my claims about how old the name “Catholic Church” is. Here are the Church Fathers on the Church:
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.
- St. Ignatius, Epistle to the Smyrnaeans
We say that both in substance and in
seeming, both in origin and in development,
the primitive and Catholic Church is the only
one, agreeing as it does in the unity of one faith
And if ever thou art sojourning in any
city, inquire not simply where the Lord’s
house is–for the sects of the profane also
attempt to call their own dens, houses
of the Lord–nor merely where the church
is, but where is the Catholic Church.
For this is the peculiar name of the holy
body the mother of us all.
- St. Cyril of Jerusalem, *Catechetical Discourses *
Now it [the Church] is called Catholic
because it is throughout the world, from
one end of the earth to the other.
Whether they wish or no, heretics have
to call the Catholic Church Catholic
- St. Augustine of Hippo, De vera religione
Notice: Not a mention of “Orthodox”.