Thank you Rebecca, I found your response really interesting, especially the Saxon link to oak which reinforces the view of a historian I spoke to about it.
I still believe in an English origin for some of the Eakins and a Celtic origin for others. The name itself is self-evidently English/Anglo saxon and can be traced back to at least the 16th Century in the English Midlands where the name is also interchangeable with Ekins and Ekin (Ekins' outnumber Eakins' by about 10:1 before 1800). Eakins' in England is pronounced with a silent 'a', like Ekin and Ekins.
Personally, I think that it is a mistake to lump together all the various spellings and pronunciations of the name, eg. Ekins, Eakin, Ekin, Ekins, Aiken, Aitkens, etc. There are marked differences in pronunciation, geographic distribution and ethnicity so there are likely to be a number of origins.
By the way, I've been to Kyle Akin/Kyleakin (before they built the bridge) and spent a little time looking around at local names. Its a beautiful part of the country and I would recommend a visit. While it is possible that one or more of the various permutations of Aiken may have come from there it seems very unlikely that all the different permutation of the names come from there. It has always been a very small settlement and is very Celtic. I'd be surprised if there had ever been any Anglo-Saxon influence on the area - Irish Celtic or Norse is more likely. By the way, do you know the Scottish Celtic or Irish Celtic word for 'Oak' - this would be really good to know. The word may have the same root as the Ulster Celts (the Scotti) invaded and occupied much of the west coast of Scotland in the Dark Ages and gave their name to the country.