Grant is a Scottish clan name.  But there has been no agreement as to where these Grants came from; nor where in fact the Grant name came from.

Some have maintained that the Grants were of Norman origin, having moved north from England in the 13th century.  However, this theory has been increasingly discounted.  Instead, a Norse origin is now thought more likely.  This was always part of the Grant oral tradition.  And recent DNA analysis would seem to support this idea.

If the Norman origin is to be discounted in Scotland, then a French-type root such as "grand" or "le grand,"  meaning tall or large, is unlikely.  So too would be the Anglo-Saxon grant, meaning crooked or bowed.  Grant tradition has suggested that the name may have come from Sliabh Grianas, the name of a meadow above Aviemore in the Scottish Highlands.  And the Norse gran, meaning a fir tree, has also been mooted.

In old Irish, grandha signified ugly or ill-favored, grande dark or swarthy.  From these roots may have come clan Grant and the sub-sept clan Chiaran....full article and link to the miscellany page.