McBeth's mother

By what right did McBeth claimed the Throne of Scotland? Was his mother the
sister of Malcolm II McKenneth? What was her name?

taf...

There are several answers to this. First, a somewhat late chronicler
calls MacBeth the nepos of Malcolm II. As nepos can mean grandson,
nephew, or even simply kinsman, reconstructions abound. Based on his
earlier documented activity, I think it less likely that he was
grandson and hence a contemporary of Duncan, but his role could be due
to his leadership of a semi-autonomous principality. That his mother
was a sister of Malcolm fits with this description (and I should
probably take this opportunity to point out that the name usually given
her appears to be a late invention) but, as i said, the source is late
and imprecise.

Second, he married Grouch, whose father had the same name, and is
usually identified with a scion of the Scot royalty, which practiced
tanistry and had been alternating among branches for some time prior
(although the tanistry system, as we understand it, did not allow
female-line succession, let alone jure uxoris claims).

Third, and perhaps most conclusive, he knocked of the prior king and
ran his children out of the country. Under the tanistry system, some
other male-line descendant of Kenneth MacAlpin, should have been
selected to succeed Malcolm, but there were slim pickings, even none,
in part because of Malcolm's efficiency in eliminating challengers.
This allowed him to attempt to establish a more linear succession,
passing the crown to his maternal grandson Duncan, but it was not like
the succession after Henry VIII, where the nobles gave him the ability
to reorder his own succession. Malcolm wiped out all comers, and then
tried to establish a new system, but in the process also opened it up
to challenge by just about anyone with a sufficient following to make
good on the claim, which MacBeth did. His was effectively the same
right to rule as Canute's.