According to the linguist E. Bascuas, the toponym Órbigo, would come from a Paleo-European hydronymic theme *urw-, derived from the Indo-European root *er- 'flow, move', with a hydronymic meaning.
The first mention is from Hydatius "Ad fluvium nomine Urbicum".
[1] The name could also have Basque roots, from the words "Ur" (water) and "Bi" (two).
There exists a theory that the river now called the Luna should be the real start of the Órbigo.
This article related to a river in Spain is a stub.