"He does not want wine."
Translation:Dydy e ddim eisiau gwin.
Because it's a negative sentence.
"to be" (bod) in negative sentences usually starts with a d- (all that's left of a negative particle nid in earlier forms of the language), though sometimes you can't even see that (e.g. you might see both dydw i ddim... and the shorter dw i ddim...).
As a side note, nid is still used in (written/non-colloquial) Welsh in some contexts, such as nid arnoch chi mae'r bai (you are not to blame).