The device cross patee fitche known sometime as the cross of Cadwallader as it appears on the great seal of James I of Scotland and sometime as the cross maltho de Caldwell on the arms of one of the English families is not a device of the Englsh King Edward as David Caldwell suggests.
I do not hold this as being the origin of the name Caldwell although it is an interesting theory.
My standpoint is that until someoe comes up with a better proof than the Cold-Water theory it must stand.
The Cadwallader theory is efectively overcome by the fact that it is a Welsh name and does not appear to have the currency on Scotland that would indicate its widespread use.
My comment is to point out for what it is worth that the Scots King used the device on his great seal in association with the cross of Edgar (not Edward) and the English armorial bearings of one of the English families also used it and had the "cheek" to call it the "Caldwell Maltese Cross". I cannot see how this woud have happened unless the English Caldwell name had been transformed from the Welsh Cadwallader in which case it would have been rational and reasonable to chnage its name from "Cadwallader's Cross" to "Caldwell's Maltese Cross".
The Stewart King's ancestors came from the same region as Cadwallader who is recognised as both the last British King and a Christian King. Perhaps the Stewart's believed that they had some of Cadwallader's blood in their veins.
The Caldwell's are supposed to have come to Scotland in the train of either the FitzAllan's or the de Moreville's (or both). Had Cadwallader's family become vassals of these families?
The de Moreville's are sometimes said to have come from Yorkshire but I have also seen it said that they came from Shropshire like the FitzAllan's.
I still have no answer on how Cadwallader could become Caldwell other than the names have some similarity. Cadwallader was a personal name and not a family name.
Back to Scotland - I am finding it hard to believe that so many Caldwell's have sprung from what is effectively an Estate and not even a village. They outnumber by a considerable degree the English Caldwell family which has a number of villages to give them their name and their origin.
The argument for Anglo-Saxon Cold-Water holds well for the English family. For the name to have sprung up in Scotland from similar reasoning is to say that the property in Scotland was either named after a Caldwell from England (which is not likely as it was usually the other way around) or sprung form the naming of that particular Estate by an English-speaking person. This is quite possible however it was the estate of one family and had to be numerous enough by the 1300's when it was alienated to another family to have given us enough base Caldwell-named population to create the large numbers of Caldwell's just a few centuries later. Again this is possible.
It is also possible but highly unlikely that large numbers of Caldwell's moved to Scotland from England.
I have many theories on the name - I favour Caerwall or Carwall as you can see but none of these theories has conclusive proof for me. Cold-Water is the most persuasive but I will keep looking as I m still not 100% convinced.