I asked scotlandspeople if they could make the image clearer, and said that the surname did not exist, and got this really helpful reply, agreeing with what has been found:
'The name as recorded on the page does appear to be "Blawlean" but I suspect it was taken down by the registrar as it sounded. Whilst I have no concrete proof, I think it may be "Blain" as there is a son born to a Joseph Cook and a Mary Blain in 1832, also called Joseph Cook. His father's occupation is "quarrier" and this matches the occupation recorded on Jean Bisset/John Cook's marriage entry in 1858. In the 1841 census Joseph is an "Ag(ricultural) Lab(ourer) & stonecutter" in Dumfries. They later seem to have ended up in Kirkmahoe.
Whilst I can't definitely say that Mary's maiden name was meant to be Blain I would say it is quite likely.'