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The shapeshifting fish part reminds me vaguely of Neds Newt, but this may be too recent.
"And as long as a sack of shit is not a good thing to be, chivalry will never die."This may be a stretch since the fish doesn't shape shift, but is it Stanley? It was on the Disney channel from 2001-2004, in the "Playhouse Disney" block, and it involved a boy named Stanley with a pet fish and dog.
The fish was named Dennis.
Edited by originalhobbit It's a good thing our last name isn't Drew, because then you'd be Nancy Drew and I'd be Andrew Drew. -Andy Botwin

I actually don't remember this one myself, but my dad does- he remembers me watching it when I was little. I'm in my teens, so don't go looking for something from the eighties or anything.
From what he can recall, there was a kid (male) with a dog and a fish(?), and he swears the fish was named Dennis. The dog looked kind of like a bulldog, and the fish could shapeshift or something. It might have been an animal-based show.