The names DAMON
have been (obvously by mistake) associated with the Greek word "daimon". This can mean "spirit of the dead", "a god who affects the fate of a person", "fate" (positive or negative). The word "demon" derives from "daimon", so this is probably the reason, why DAMIAN
is sometimes associated with the devil.
In the New Testament the word "daimon" appears only once (Matthew
8,31) and there it means "demon" indeed. The usual word for "demon" is "daimonion", which is of course related.