"Jason"? I don't think that is biblical...
To reiterate what has been pointed out, "Jesus" is the same name as "Joshua", and means something like "God saves". It would therefore have been a very appropriate name for Jesus from a Christian point of view and one can understand why they imagined that God had commanded that he be given this name (Luke 1:31). It was, however, also a perfectly common name at the time, and we know of various other Jesuses. For example, Jesus son of Ananias, who according to Josephus made a prediction of the Temple's destruction in the 60s and got arrested and flogged for it.
People in Jesus' day did not have surnames - they had patronyms, in the form "bar [father's name]". (That is the Aramaic version; the Hebrew version is the more familiar "ben".) The most obvious example from the New Testament is Barabbas, whose full name, according to Matthew 27:16, was Jesus Barabbas (so there's another Jesus for you). He was Jesus son of Abbas. Our Jesus would have been known in his lifetime as Jesus bar Joseph (or, rather, Yeshua bar Yosef). Alternatively, people were often known by their place of origin or association, which is why he is also Jesus of Nazareth.
"Christ" is simply the Greek version of "Messiah", meaning "anointed". If Jesus himself ever used the term, he would have said "Messiah" (or the word that this is a transliteration of). It is unlikely that Jesus regarded himself as the Messiah or talked about it much, a fact which is reflected in the Gospels, where only once does Jesus ever explicitly claim to be the Messiah (Mark 14:61-62) even though the authors of the Gospels are quite clear that he was the Messiah.
Christians certainly believed from a very early stage that Jesus was the Messiah and they seem to have called him "Christ" as if it were his name from an early stage too. If you look at 1 Thessalonians, the earliest book of the New Testament to be written, you will see that he is called "the Lord Jesus", "the Lord", "Jesus Christ", "the Lord Jesus Christ", "Christ Jesus", and simply "Christ" interchangeably; although bear in mind that in Greek proper names carry a definite article (e.g. you would literally say "the Paul" to mean simply "Paul", and similarly "the Jesus" to mean simply "Jesus"), so in Greek there is not quite the grammatical distinction between a name and a title as there is in English. When Paul says "the Christ" (ho christos) it is not quite clear whether that is a title or a name, since it would have the definite article either way. However, the various names mentioned above seem to be used completely interchangeably, and in particular, "Christ" is used even when there is no particular reference to his messianic status or function. So it has basically become a name.
Jesus and his family would have spoken Aramaic. It is possible, but unlikely, that Jesus knew a little Greek as well. However, scholars disagree over the extent to which someone like Jesus, and Jesus in particular, was familiar with Hellenic or Roman culture; the basic problem being that there were certainly Hellenic cities in Galilee at the time but they do not feature in the Gospels at all.
[EDIT Looks like other people said most of this while I was writing it...]
