Except Satan isn't a proper name, it's a common noun like "dog" or "cat" or "god". It simply means "opposer". In a similar vain, "devil" meant "slanderer". So basically Jesus is saying, "Piss off, my enemy. I don't like what you say." It wasn't until Zoroastrianism crept into Christianity that Satan and Devil became proper names. Christianity at the time of the King James Bible was way more varied than it is today, with some sects being way out in right field. In order to get the various sects to unite under one church, there had to be some give and take in doctrine and thus Satan the Angel-Turned-Devil came to be. Some sects of Christianity don't believe in the existence of Lucifer (a Roman loan word) and some don't even believe that Satan as a single entity even exists. And all the evidence points to Lucifer/Satan being an adoption of Ahriman into Christianity, just as Beelzebub/Baal was adopted. And why would Jesus refer to Satan and Beelzebub in separate references? Why not just straight up say, "If Baal also is divided against himself--"? Just as Lucifer is a mistranslation of an honorific title of a Babylonian King simply meaning "(Planet) Venus" (I don't get why it's so hard for people to grasp that concept. Why, of all the deities in the Bible, would only one deity have a Roman name? It's obviously a mistranslation, but it's heresy to say the Bible wasn't translated correctly.), "satan" is just a title he used to refer to any heretical deity. Beelzebub was the most famous in his time and it was the one pharisees accused him of calling on, not because Beelzebub is Satan. It's that same kind of spin doctoring that makes political races in Democratic countries a deplorable mockery of the original ideology. And of course the great dragon would be called "devil" -- he spun lies to get Eve to eat the apple and share it with Adam -- and "satan" -- he opposed God's will and creation. And the whole irony of Revelation is people insist the dragon is The Devil proper, yet Lucifer is depicted as a beautiful archangel or serraph. Wait, was he an angel or a dragon? There are so many inconsistencies in Revelation. Even if you take from the Apocrypha, which is also heresy to ascribe truth to, then it just becomes apparent that Christianity borrowed from other religions and is no different than the religions of the barbarians and other heretics. And even the Jews complained the original Western translations of the Old Testament before Jesus' time were very faulty. Different authors ascribed different interpretations of the Old Testament. It's just like if you took a book written in Japanese or Chinese and asked a class of students to translate the book. Each translation will vary and some will be so far off that it's almost not even the same story. Yet many Christian churches had to rely on those texts because it was the easiest way to read old scriptures, so from there they interpreted the New Testament as they saw fit. Even Jesus' disciples had their own understandings of the religions of that era. Judaeism and Christianity were not unified (within their own disciplines, I mean) religious beliefs, there were numerous sects each with their own scriptures and each with their own interpretations and translations of scriptures.
He's probably called the Prince Of Darkness because Beelzebub was likely a bastardization of "Baal, Lord on High" or "Prince of Baal". And for that matter, why would Satan only be a prince of darkness? Who's the king or monarch or emperor or lord or duke of darkness?
But I think I diverged from the topic too much.