The Bible actually states:
"You will be with child and give birth to a son, and you are to give him the name Jesus." (Luke 1:31, NIV)
Fortunately for those in Jerusalem in the years before Christ, there was never a huge discrepancy as to what last name or surname, Jesus should have had. Surnames actually evolved much later for much of the World but came into being in different times for different cultures. The Chinese had them quite early, the 5th century BC., in fact, and in cultures where clans were important, it was probably earlier too. Their surnames were an expression of allegiance to the central clan hierarchy,(as in the Scottish and Irish) or a means of telling who was a possible marriage partner.(eg the Batak of North Sumatera whose first question to anyone traditionally was not 'how are you' but "marga apa?" " what clan?") The English began to take on surnames in the early middle ages (11th century), starting with the Norman elite, who took theirs from their place of origin or,in the case of younger sons, from the manor they owned. By 1400 most English had surnames, either from the physical characteristics of an ancestor (Black, White, Short) or their ancestor's occupation (Smith, Archer) family relationships (Johnson, Watmough-kin of Walter-) or nicknames (Pennyfather-miser). The highland Scots and the Welsh did not have fixed surnames until as late as the 19th century in some areas, as they used the son of system (mac in Scotland, ap in Wales). Some of the Irish surnames (with o' prefixes) also fit this category, but they were fixed at an earlier time, because of the conquering of Ireland by the Normans. In many parts of the world, there are no surnames at all...In Indonesia, while tribes such as the Batak and the Toraja have clan names that are used as surnames, the numerically dominant Javanese have none traditionally, although they are gradually being adopted. The Balinese do not have them, and are maintaining the custom. Most of them, being Bali-Hindus, know their temples of origin, and detailed descents are considered unnecessary. Insted of surnames, they have a complex naming system, involving titles of caste, position in family, formal given names and home names.
It is not surprising then that one of the first issues that come up to sometimes surprised expectant unwed parents is what last name their baby will take on. While there is not a steadfast law which states whether it is the mothers surname or fathers surname that belongs to the child upon birth, the Courts have typically looked at the birth certificate as bearing the surname chosen and contracted by both biological parents. The ultimate decision to later change a last name creates the burden on the parent who is trying to change the name to prove that it is in the best interest of the child to have a particular last name. In the case of Mageira v. Luera, the mother had custody of her son for a continuous three year period. She petitioned the Court for child support from the father when the child was approximately four years old. The Court granted support from the father but then granted the request of the father that the childs last name should be switched from the mothers surname to the fathers name because the father was “paying for the privilege”. The Supreme Court said later that children do not bear the name of the father simply because a father pays support but rather because it is in the best interest of the child to have one name or another.
 Mageira v Luera, 106 Nev. 775 (1990)