If you go to any mass at a church under the Vatican, at mass they will commemorate the pope of Rome, and then the local bishop. This is also a change, an important one, that the Vatican has instituted in a practice called the diptychs, and the Orthodox practice is still as it was in the first millenium: when I go to Divine Liturgy, the priest has a cloth, called the antimens, with means (in Latin!, the term came about when both Old and New Rome used Latin officially) “instead of the table” i.e. the bishop’s altar. It is signed by the bishop, given us permission to celebrate Divine Liturgy on it, because the bishop is the oridinary minister. As St. Ignatius writes:
Wherever the bishop appears, there let the people be; as wherever Jesus Christ is, there is the Catholic Church. It is not lawful to baptize or give communion without the consent of the bishop. On the other hand, whatever has his approval is pleasing to God. Thus, whatever is done will be safe and valid. — Letter to the Smyrnaeans 8,
Now at Divine Liturgy the priest commemorates our bishop (Mark, a former Pentacostal, btw) and our primate (Phillip) of the Autonomous Archdiocese of North America, to show our communion with our bishop and the head of the synod to which he belongs. Where Bishop Mark celebrates, he has no antimens (as bishop, he needs no permission) but he commemorates all the bishops of the archdiocese and and the synods head, Metropolitan Philip, to show their communion. When Metropolitan Philip celebrates DL, he commemorates the heads of all the heads of all the Archdioceses/synods of the Patriarchate of Antioch, and the Patriarch, Ignatius IV (the 163rd successor of St. Peter in his first See, Antioch). Patriarch Ignatius at DL commemorates all the other patriarchs of the One, Holy, Catholic, Apostolic and Orthodox Church. This practice of diptychs is meant to show the unity of the Church throughout the world, and as a sign of who is Orthodox. When someone is struck from the diptychs, it means that bishop, and all who commemorte him, are not in communion. This happened recently with the patriarch of Jerusalem, who had been mismananging Church property amongst other problems. The synod of Jerusalem, met, struck him from the diptychs, the other patriarchs, investigating the situation in a synod of their own in Constantinople supported the synod and struck him from the diptychs, and he was deposed. It also happened in Moscow, where the argument with the Ecumenical Patriarch of Constantinople reached a point that the PoM struck the EP from the diptychs. The other patriarchs, however, told both of them that they, the remaining patriarchs, were striking neither from their diptychs. So they were going to keep them in one Church so they had better come up with a solution, which they did.
Now, in the diptychs as modified by the Vatican, the pope of Rome’s name is mentioned at every mass in every church all over the world. In the Early Church, we don’t see that: no Church in Egypt, for instance, commemorated the Pope of Rome except the Church where the Pope of Alexandria was celebrating Divine Liturgy. The Vatican sends out who is in the diptychs, and he alone decides the list. In the early Church, it was not so, and Popes of Rome on occasion were struck from the diptychs: for instance the date 1054 is really not the correct date for the schism, but has been promoted in the West. For the Orthodox, the split occured when Benedict VIII inserted the filioque (at the emperor Henry II’s demand) into the Creed recited at the DL. When the EP received the notice of Benedict’s ascension with the filioque in his confession, the pope was struck from the diptychs. (The Universal Ecumenical Councils had forbidden altering the Creed on the pain of deposition). One of the issues of the delegation from Rome in 1054 was to insist that the other Patriarchs put the pope of Rome back into the diptychs.