sadnil,
It seems that it could be anything!
I note that your ancestor's is the only appearance in the IGI of a name with spelling MCCLACKLIN. And unfortunately - though they had quite a few children - Ann's maiden name is not given in their birth/christening entries.
It does look like a version of the widespread name which is spelled in various ways e.g. McLACHLAN, McLOUGHLIN, McLAUGHLIN, etc (or Mac!). And that name goes way way back. I think it would not be prudent to make any guesses about Ann's origins without further information. And I would not draw any conclusions at all from use of Mc, Mac or M' (I have about 80 variant spellings for the Scottish name McLaws/MacLehose including Mc, Mac, M' (not to mention the same name starting with Mickle, Meikle, Muckle, etc, etc).
Have you looked at the film with the Parish Register entry for their 1806 marriage? The name may have been wrongly transcribed. Also, perhaps you just might be lucky enough to find that the entry gives some other clue (unlikely but you never know ...).
As they were still in Whitby when their children were born, perhaps they were still there, and Ann still alive, by the time of the 1841 census - have you looked up the 1841 census? If you find her, that should at least give you a clue to her birthplace and age. Even better if she survived until the 1851 (though I see that FreeBMD has an Ann WINSPEAR dying in Whitby in 1849).
If you have not looked at these censuses, perhaps a lookup request on the Yorkshire, North Riding board would be a good idea - it certainly looks as though people have been helped with the 1851 census (though not the 1841? - But, who knows).
Cheers,
Judy
PS: you mentioned a Catherine in much later censuses in Whitby. Is she related?
