I have just come across your original posting on DOW.
My limited knowledge suggests that the name originated in various parts of Scotland and the British Isles independently, as you could expect for such names as Baker/Baxter and Smith.
This appears to be confirmed by its occurrence in some concentrations such as Aberdeenshire and Perthshire in Scotland; and also in Essex in England at early dates.
There are the Dow Caves in Yorkshire; and the Dowgate ward/area of London lying between Cannon St Station and Tower Bridge.
It and variants can also be found in Wales and Ireland as persons' names and as part of place names.
It is only relatively recently during the past 10 years that I have come across the suggestion of it being derived from DOVE. If memory serves me correctly, this is from one record apertaining to Berwick-on-Tweed.
The more usual and to me, likely derivation is from Dhu meaning black; and its corresponding versions in Erse, Welsh etc.
This would also tie in with the generally accepted derivation of the wide-ranging name "DEVON" derived from "Black Water". See also "AVON".
There are several River Devons scattered around Britain.
I have also seen the suggestion that for some Dows, it derives from a word meaning "can do", implying ability etc.
Beyond that, I have come across Lebanese DOWs mentioned on the Web.
In Edinburgh, there was/is an oriental gentleman whose anglicised (Scotticised?) name DOW is apparently from TAO. He worked in the same establishment as my almost identically named female cousin, causing confusion at the switchboard.
Then also on the Web, there was the declared anglicisation of "D'Aoust" to DOW.
To the extent that I have traced, my DOWs are mainly from the Edinburgh area; but subject to any subsequent research, I work on the background assumption that they arrived there by migration probably from Perthshire.
For the locations mentioned by anyone, within Britain, go to-