the nbame MACDOW (and variants) virtually does NOT exist in Scotland.
You can confirm this by using the Free Surname searech on Scotland's People; or by using the LDS Family Search site.
From the latter, the name MACDOW is confined to North America, present-day USA and Canada.
Scotland's People accesses the official records of BMDS for Scotland back to 1553, so if the name had ever existed in Scotland, it would show up on SP.
The LDS FS Site produces 1 (one) MacDow in Scotland; compared to a raw total of 1,436 for North America.
s a DOW myself, I encountered two older explanations of its source-
q from the Gaelic "Dhu" or similar meaning "black", this clearly lines up with the Welsh Gaelic DDU also meaning black;
2 possibly from "Doot" meaning capable of doing it.
It is only in very recent years that I have seen the suggestion that it is from DOVE; and that was limited to Berwickshire, where very few DOWs or DOVEs lived.
One suspicion come to mind was that this was from the misinterpretation of thw final "w" having a "curlesque" at its end, so in hand-writing, the final "w" resembling "ve".
Having seen many erroneous transcriptions of ancient documents over the years, the latter would not surprise me.
There are various locations down in England where DOW clearly is connected with "black", such as the DOW Caves in the Peak District and DOWGATE in the middle of London leading down to the Thames, very close to The Tower, its origins being in the dark/black filthy residues coming from the various tanning yards that used to exist there - and the Livery Hall of the Tanners is still situated there.