Edition: Michael Joseph, 1982
Dorothy Dunnett's novel of Scotland in the Dark Ages concerns the historical Macbeth - or does it? She certainly knows more about the situation in eleventh century Scotland than Shakespeare did (Macbeth ruled just before the Norman conquest of England), but her plot relies on an identification between two historical characters. Macbeth, she assumes, was in fact the baptismal name of the Viking Earl of Orkney, Thorfinn II.In some ways, this works quite well: Macbeth is a likely candidate for a Gaelic baptismal name (it means "son of life"), though a saint's name might have been more likely; Thorfinn was descended from the kings of Scots and would have had at least as good a claim to the throne as the line which eventually established itself (both related to earlier kings through descent from daughters of Malcolm II); the interest in Orkney makes him plausibly involved in an attempt to unify Scotland, which provides an interesting political aspect to the novel; his Viking background paves the way for a clash of cultures, also of interest to the reader.
There are, however, arguments against the identification of Thorfinn and Macbeth, and the subsidiary identification of Ingeborg, Thorfinn's Norwegian wife, with Gruoch, more commonly known as Lady Macbeth (which is also done with the baptismal name device). The way the Scottish kingship generally worked at this time was that the succession alternated between groups of cousins, patrilineal descendants of Kenneth MacAlpine, who had originally united the kingdom. This system meant that minorities, the perilous rule of underage kings, was avoided, at the cost of making murder by a cousin the most likely way for a Scots king to die. Macbeth was one of the last kings to gain the throne in this manner; Malcolm III, who killed Macbeth, basically managed to stabilise the succession in his own descendants (barring short usurpations by Lulach - a relation of Gruoch's - and Donald I - Malcolm's brother). This was partly achieved because Malcolm held onto the throne for a considerable period, during which he killed most of the other potential candidates for the throne.
Now, both Macbeth and Gruoch are provided by the Scots chroniclers with lineages connecting them with the Scottish crown, which do not match with those existing for Thorfinn and Ingeborg. While it is clear that such lineages would be invented by usurpers to give them a claim to the throne (there are several instances of this in the Anglo-Saxon Chronicle, for example), the way that Dunnett has set things out in her book makes Thorfinn's main claim to the throne his mother's descent, while the chronicles imply that Macbeth's is his father's, whether real or spurious.
Another objection to this identification is that Macbeth is known to have died in 1057, while Thorfinn is thought to have lived rather longer, until about 1065 (though the exact date of his death is not known). I don't know what the evidence is for assuming the later date, but it is that given by Tapsell's Monarchs in the table listing the Earls of Orkney.
The methodology of an academic historian would require that an assumption such as the identification of the two men is not made without supporting evidence. The less you assume, the less you can get wrong. As a historical novelist, you can make any assumption you like which can help your story, so long as it is reasonably plausible. The assumption Dunnett makes here drives an interesting novel, though a very long one - Macbeth reigned for seventeen years after all, not the few months that is the impression left by Shakespeare.
Less acceptable is the way that Dunnett attempts to force Thorfinn/Macbeth into the mould of the heroes of her historical series, Lymond and Niccolo (both of whom are fictional characters). Thorfinn is made to have almost exactly the same characteristics as these heroes. The character may be fascinating, and equally something of a superhero, but the three men should certainly be different from each other.