The title of 'Pope' has been in continuous use for the Patriarch of Alexandria since about 240 a.d. first used for Pope Heraclas of Alexandria. Pope Shenouda is the Coptic pope of Alexandria while Pope Theodoros is the Greek Orthodox pope of Alexandria.
I'm almost positive that the imposter Coptic Catholic Patriarch Antonios Naguib does not, nor is allowed to use 'pope' for himself based on strict orders from his boss; Pope of Rome .
Yes, you are correct on that, nor can the Melkite Patriarch who is also Melkite Patriarch of Alexandria use it, nor the Latin one who was abolished (Latin Copts do exist). Their church is not big enough for two Popes, unlike the Early Church.