Upvote:1
Your question assumes that the church founded in Rome was the Roman Catholic Church that it is now. During at least the first 400 years of Christianity, the Bishop of Rome was just another bishop - the universal church was not governed by one person (ie the bishop of Rome or the bishop of anywhere else), but instead by consensus among the different bishops (ie the Church Fathers) in the different cities of the empire. The Roman church, because of its size and resources, but also because of its preeminence as the capital of the empire, slowly took on more authority.
By the time Christianity was legalized by Constantine in the late 4th century AD, the catholic church (that is the "universal church", which is what catholic means) was governed by the churches thought to have the most importance, namely: Jerusalem, Alexandria, Rome, Antioch, and Constantinople. This is attested to by the Nicean council and the following general church councils in the next 200 years.
We can say safely that therefore, at least for the first 400 years or so, the Roman church only shared rule over the church, and people would not have considered themselves to be 'Roman Catholic', as the nomenclature wasn't in use yet, and the idea of an exclusively Roman run church was anachronistic.