Interesting question.
I consulted Fasti Ecclesiae Scoticanae on this.
Christian Guthrie Carnegie (1803-1865) was the daughter of Alexander Carnegie of Redhall (1762-1836), minister of Inverkeilor, and Elizabeth Skirving (d 1835), whose father Adam Skirving (1719-1803) was a tenant farmer at Garleton in East Lothian and wrote, among other things, the song 'Johnnie Cope'.
Alexander Carnegie was the son of John Carnegie (d 1805), minister of Inverkeilor, and Catherine Walker (d 1790), whose father was William Walker, farmer in St Fort in Fife.
Christian was the eldest daughter of Alexander Carnegie and Elizabeth Skirving, and their sons were named John and Adam, suggesting that they followed the naming tradition. In which case, you might expect Elizabeth Skirving's mother to have been Christian Guthrie. I can find no evidence for this, however.
There is, in the National Galleries of Scotland, a portrait of Adam Skirving bequeathed in 1901 by David Ainslie, and I note with interest a marriage of an Adam Skirvine to a Jean Ainslie in Athelstanefore in 1748. The artist was Adam's son Archibald Skirving (1749-1819), who also painted several notable persons of his day. This David Ainslie was probably the son of William Ainslie and Martha Skirving, baptised in Leith in 1813.
Adam Skirvine seems to have been born in Athelstaneford, son of Archibald Skirvine and Grizel Howden (spellings vary!). In 1803 a David Skirving married an Elizabeth Carnegie in Athelstaneford; their first son was Adam, but their daughter was named Janet so Elizabeth's mother was probably not named Christian.
So there is no obvious family reason for Alexander Carnegie and Elizabeth Skirving's first daughter to be named Christian Guthrie.
There is no Christian (or variants) Guthrie in any part of the extended family of the Rev Thomas Guthrie until his eldest daughter Christina, plainly named after her maternal grandmother Christina Chalmers, was born at Arbirlot in 1833.