Here Virginia Woolf is speculating on imaginary names for the narrator of her story, the 'I' of the text from this point onwards (see discussion in Spark Notes). As with the fictional names for the university and the college, their purpose is to emphasise the generality and universality of what the narrator is saying.
Mary Beton is the name given by Virginia Woolf both to the fictional aunt of her narrator, whose legacy of £500 per year enables the narrator to live independently, and to the narrator herself. It is the name (usually written, Mary Beaton) of one of Mary Queen of Scots' four ladies-in-waiting (all of whom were called 'Mary'), as is the next name, Mary Seton (which is used later in the text for the narrator's friend at Fernham). However, Woolf does not go on to refer to Mary Queen of Scots' two other ladies-in-waiting, Mary Fleming and Mary Livingston, but to Mary Carmichael, a name mentioned in a ballad written in the Scots language generally known as 'The Ballad of Mary Hamilton'. Various versions of this exist, but they all refer to a Mary Hamilton who is a lady in waiting to another Queen of Scots, and who has been condemned to death for killing a baby, the result of a liaison with the King of Scots. The verse is confusing as the first two Mary's named were ladies-in-waiting to Mary Queen of Scots, whilst the other Mary's referred to (Mary Carmichael and the narrator, Mary Hamilton) were not.
Verse from one version of 'The Ballad of Mary Hamilton':
Yestre'en the Queen had fower Mary's
The nicht she'll hae but three
There was Mary Seton and Mary Beaton
And Mary Carmichael and me.
In A Room of One's Own, Mary Carmichael is the name given later in the text to an imaginary contemporary novelist. The choice of name is likely to be connected to the birth control activist Marie Carmichael Stopes who wrote a novel, Love's Creation (published in 1928), under the name Marie Carmichael.