Why he changed his name? And why Magus?
He probably didn't. In some later renderings, as has been said, Magus has been taken to be 'wizard' or 'sorcerer', though in the original Latin it means something more akin to 'wise man', and is pronounced MAH-gus (the plural being Magi) Technically, the word is not even Latin - it comes from Persia, where it was a name for their priestly class. Thus the 'wise man' connection.
Anyway, if my own theories hold in some regard, the history of the world was more or less similar to ours up until about 400AD - thus Rome existed (I take this from the existance of crosses on the doors to the church, the existance of cathedrals, and in the existance of Latin itself in several key points, ie. Angelus Errare and Res Nullem) The Mystics, being more from the East, and having at least some of that older knowledge, would probably know Latin, or at least their leadership ranks might. Seeing the power and keen mind of the child, especially later when he is grown to power, they give him the throne-name of 'Magus', ie. the Sorcerer. It shrouds him in mystery, and cements his leadership position all the more. To have a foe simply named 'The Sorcerer' is a lot more frightening than one with a name proper. Like Sauron being named 'The Necromancer'. It's a lot more chilling.
As a matter of fact, though, the name Janus (pronounced ee-AH-nuss) is interesting in and of itself, as it is the name of one of the old Roman gods who, to my knowledge, is not one of those borrowed from other people (unlike Juno, Jove/Jupiter, Mars, Minerva, etc.) From what I know, he was a god of beginnings and endings, and of doorways, signalling change. He was worshipped to, for example, at sowing and harvest, and the doors to the temple of Janus were cast upon at the onset of war, to signify a course set upon irrevocably.