To add to that, can someone give the literal answer to that question, ie what are the very first names we have written down?

This thread could probably answer some of your questions. As for surnames, I cannot point to a first apparition, but it is important to understand that the concept was reinvented several times. Basically, they appeared in patrilineal societies (because you can normally pass down only one surname — contrast the early medieval situation, where the use of components in personal names made possible to draw on both paternal and maternal familial traditions (1)), with a strong emphasis on territorial implantation (rather than clanic ties), and a limited pool of first names. For instance, we already have recorded Armenian surnames (for the aristocracy only) in Late Antiquity, because Armenian society fulfilled all these criteria. In Europe, surnames appear in the Frankish nobility in the 9th and 10th century, for the same reasons. The spread to commoners, in all these cases, is a later development.

(1) Of course, in later periods, it was still possible to emphasise your maternal line if it was more prestigious than your paternal one — however, the importance of your maternal kingroup (removed cousins and so on), and in general of horizontal kinship, was far less important than before.