Alexandria was a major center early on in Christianity... It's where the first theological school was, some even say it's where Theology was invented under Origin. In the early Church there weren't Patriarchs, there were just bishops. Each town had it's own bishop, and while some were more prominant, none were over the others.
Then the Church in Alexandria got so big the bishop start ordaining other bishops under himself to assist him, this is the first time it was done. Bishops were called father, so the bishop of Alexandria became the father to fathers, or pappa abba, or pope. At this time the church in Rome was small, and the bishop there had no authority over the neighbouring cities, which had thier own bishops.
Hundreds of yeards later the same hierarchy developped in Rome, later the bishop of Rome decided they should be called Pope when previously only the bishop of Alexandria was called Pope, and later still they decided that only the bishop of Rome should be called Pope... by that time we'd been completely sepereate for a long time, so it in no way affected us.
When the Eastern Orthodox set up a Patriarchate in Alexandria to replace the Oriental Patriarch after the split they assumed the same title.
The Coptic Orthodox Pope carries this title because of the honour of Alexandria in developping this hierarch and having such a prominant role in the early church... but the Pope of Rome is a patriarch, equal to the other patriarchs, without any of the trappings of the roman Catholic papacy...