Jane McPherson seems to have multiple name changes from Jean to Janet at different points (e.g., there is no marriage cert for a Jane McPherson to Peter Grant in the 1820s but there is one for Peter Grant and Janet Grant).
No, she didn't.
Jane/Jean are very common variants of one another. Many people will tell you that Janet is commonly used as a variant of Jean/Jane, but I have found many more families with both a Jane/Jean and a Janet/Jessie than I have come across instances of a Jean/Jane also being recorded as Janet.
If Jane/Jean's maiden surname was MacPherson, she would not be recorded as Grant. This must be a different couple altogether.
In fact it's easy to prove this.
Peter Grant and Janet Grant had at least 6 children: Alexander 1828, James 1831, Robert 1833, Elspet 1837; William 1840; Janet 1844; all born in the parish of Duthil and Rothiemurchus. As this family overlaps with that of Peter Grant and Jean/Jane Macpherson, these must be two different Peter Grants.
Jean McPherson, daughter of John McP and Christian McLean, was baptised in the parish of Duthil and Rothiemurchus on 16 July 1804.