In the prologue, the Sole Survivor has the comment "never going to find that dog".

Which got me wondering, considering they never returned to their home, did the dog just stay away and eventually sire a bloodline that lead to Dogmeat in the future?

That would be interesting, that the new pet dog (Dogmeat) is a descendent of their previous pet dog.

Its just a Fallout thing, think of Dogmeat like how Lassie keeps getting replaced - its a different dog but somehow the same.

I have not replayed the beginning of the Game since early December, but this could be a cover for how F4 Dogmeat is not an Australian Shepherd.

According to Bethesda each Dogmeat is descended from the Fallout 1 Dogmeat. I think the thing from the game opening is just a way to show the Sole Survivor is a dog person.

Dog Meat is nurse Joy.

Dogmeat is a synth....you heard it here first.

Dogmeat is the littlest Hobo and that is why he is the best companion.