I think Ash's Dad died and he's truly adopted.
I'm not joking.
Ash looks nothing like Delia, his mom.
They both have brown eyes and aren't the sharpest tools in the shed?
Close enough for me.
And not everyone is a carbon copy of their parents, i.e. Same hair color and same eye color. (Looking at you Jun.)
More "resemblance" is hard to see in cartoons.
On a different note, if Ash's dad died, why wouldn't his so called biological mother keep him?