In the Old Testament, Ishmael is the name of Abraham's firstborn son, conceived with the Egyptian handmaiden of his apparently barren wife Sarah. The child is cursed before his birth by the angel who announces it:
"And he will be a wild man; his hand will be against every man, and every man's hand against him"
When Abraham and Sarah are granted a son of their own, God orders that Ishmael and his mother be banished into the desert.
With this opening line Melville's narrator tells us three things: that his name is not Ishmael, that fate has not been kind to him, and that the following tale will be at least partly allegorical.
Online text of the Book of Genesis (Authorised King James Bible)