There are all sorts of reasons why a child may be given a name that doesn't fit the naming tradition.
Margaret is a very common given name for girls in Scotland. Why do you think the child was named after the landowner? Could she have been named after a relative who had just died?
What were the names of her grandmothers?
There is a record of the marriage of Robert Morton and Elizabeth Rennie in Rutherglen in 1844. Scotland's People has no record of a marriage of Robert Morton to Elizabeth Rae. They had at least Robert, 1849; William, 1852; Thomas, 1854; Elizabeth, 1856; Jane, 1858; Janet, 1862; Martha, 1864; Christina, 1866; and John, 1868. There is also a Margaret Hamilton Morton, mother Elizabeth Rae, in 1846.
This family was in Bothwell in 1861. Robert was 34, born in Rutherglen, and Elizabeth was 33, born Tollcross (Glasgow). Margaret is transcribed as Mary in the version I looked at. In 1851 they were in 'Village of Hamilton Farme' parish of Rutherglen.
In 1841 Robert is probably the one at New Farme, Rutherglen, with Robert Morton, 45 and Margaret Morton, 43. If this is your Robert it suggests that his mother, and hence Margaret's grandmother, was named Margaret.
Elizabeth Rennie, other surname Morton, died in Rutherglen in 1876 aged 48. You need to look at her death certificate to see what her mother's name was.