We know that 'Christ' is not Jesus' surname, any more than 'H' is his middle initial. 'Christ' is Anglicized Greek for a Hebrew term meaning 'anointed one', which in turn is usually transliterated as 'Messiah'. It is a title, not a name of the kind given by parents to their children at birth or thereabouts. But what of 'Emmanuel', a name we seem to hear about only during this season? It is not an ordinary given name and has not taken root, like 'Christ', as a title; yet according to Matthew, alluding to Isaiah 7:14, "they shall name him Emmanuel, which means 'God is with us'." Well, who is this "they"? As far as I can see across time as well as space, "they" are mostly carol-singers. Now for all I know, this or that sector of Eastern Christianity might have a tradition of calling Jesus 'Emmanuel'; if so, that would certainly answer the question. But in the last analysis, I doubt it matters much who "they" are so long as there's somebody taking a cue from the infancy narratives in the New Testament. What matters instead are two other things.
First, the interrelation of meaning between the names 'Jesus' and 'Emmanuel' is theologically significant. 'Jesus' means 'he who saves', specifically from our sins. Given that the two names 'Jesus' and 'Emmanuel' are somehow names for the same person, the significant point is that the one who "saves" us from our sins is the one who is "with us." Conceptually, that equivalence is not at all obvious. God has not saved us from our sins by decree: remotely, impalpably, and at some time in the past. Many nominal Christians carry on as though he did; but if he did, we could only acknowledge the fact in the abstract and wonder how it has do with our actual lives. In Jesus Christ, God become a man, God saves us from our sins by having pitched his tent among us with the Incarnation, by having suffered with us on the Cross, and by continuing to suffer precisely in us, as he extends the presence of his risen Body into the world through the Church. God thus saves precisely by being with us. For me, that was a breakthrough insight about the Atonement. The well-known juridical metaphor for salvation, by which Jesus' death saved us by paying an infinitely great debt to an infinite creditor, is destructive when taken too literally. What Jesus really did, and does, is invite us to re-integrate into divinity by being intimately present to us in every moment of life—no matter how small or large, no matter how nasty or glorious—and soliciting our 'yes'. If and when forthcoming, that response is punctualized and fortified in the sacraments, above all in the Eucharist.
The other point which matters is that biblical literalism is dangerous. In the past I've made much of the fact that Matthew's use of Isaiah 7:14's reference to "a virgin"(Septuagint: parthenos) is not warranted as a strict deduction from the original Hebrew text but only as an inspired abduction. You can't get from there to here by being merely literal. Similarly, 'they shall call him Emmanuel' is not true if taken as a prediction about what Jesus would be normally called by name, or even by title. Its truth consists in its being a proleptic summation of what Jesus is for us. It is the Gospel-in-germ. That of course is not the "plain sense" of the term for the ignorant and the literal-minded. But it is the plain sense for those who read today's gospel in the context of Tradition and the teaching authority of the Church.