Alistair Campbell of Airds, in his book "A History of Clan Campbell, Volume 1 From Origins to Flodden" mentions this theory. However, Alistair says that "all the early charters spell the name Cambel, and the 'p' does not appear until the fifteenth century
I have also found reference to the first Campbell being Archibald, the son of
Malcom MacDuibhn (the second) and Cambus Bellus Beauchamp who married in Normandy.
I cannot verify that this is true.
It appears common in those days that if the mother was royal or otherwise significant, the child sometimes takes some form of the mother's name.
They came to Scotland where Archibald Campbell married Eva O'Dwin, thus starting the long CAMPBELL clan.
Eva was the daughter of Paul A Soporren MacDuibhn.