The diocese of Rome. There is a bishop heading every diocese. But surely you know this.
The city of Rome is not the diocese of Rome. And surely you know that too.
You know and I know that I know the distinction. Still, the Catholic Church is frequently identified with Rome especially prior to 1870 when they lost their last armed war.
Perhaps it would be better to eliminate all "official" identification with "Rome", "Roman" or the like.
For example:
CCC
2089 Incredulity is the neglect of revealed truth or the willful refusal to assent to it. "Heresy is the obstinate post-baptismal denial of some truth which must be believed with divine and catholic faith, or it is likewise an obstinate doubt concerning the same; apostasy is the total repudiation of the Christian faith; schism is the refusal of submission to the Roman Pontiff or of communion with the members of the Church subject to him."
Hmmmmmmmmmmmm The ROMAN Pontiff.