Character is trying to learn magic from very old wizard. It turns out the wizard is hurting his students when they are ready to graduate. Main character defeats the wizard because he is his son and they share the same secret name. The reason was that the father wanted to place his soul in the son's body but the son had been saved by his mother.
Somewhat reminiscent of The Scion of Abacus.
The character is the son of a thousand+ year old wizard, who serially kills and takes over the bodies of his offspring to extend his own life.
I don't recall enough details to remember if the mother comes in though. This is also a fairly recent book so it may not match depending on your timeframe.
Erragorn, although its the later one of the three books.