Answer
The name Alasdair mac Mhaighstir Alasdair translates to "Alexander, son of the Master Alexander." It's a patronymic name common in Gaelic cultures, where the first name is followed by the father's name and a patronymic suffix like "mac" (son of) or "nic" (daughter of). In this case, Alasdair's father was also named Alexander, hence the repetition of the name.