I've come upon numerous instances where a pre-11th century person or artifact is associated with either the Orthodox or Catholic church. The most recent example is in Francis Fukuyama's "The Origins of Political Order", where Gregory I is titled "pope of the catholic church" and where further the "influence of the catholic church in Europe in the 7th century" is discussed. The wikipedia page about [Gregory I](https://en.wikipedia.org/wiki/Pope_Gregory_I) also states that he was a "Pope of the Catholic Church from 3 September 590 to 12 March 604 AD".

Technically, at that time before the Great Schism, there were no major denominations in the Christian church. For example, the pope should be considered the Patriarch of Rome, equal with the other patriarchs. While I'm aware that "catholic" can mean "universal", these instances are clearly in the modern connotation of a Christian denomination and are not exclusive to the Catholic faith, but also prominent in the Orthodox case.

What should we call the pre-schism Christian church today?
Or, if there is an accepted name, why isn't it used instead of Catholic and Orthodox when referring to events, people, etc. before the Great Schism?