Delilah is a British dog and is the great-great-granddaughter of Pongo and Perdita . She's married to American dog Doug. Together the two have a total of 99 kids from their previous marriages, some of the 99 Dalmatian puppies that appear on the show are descendants of Pongo and Perdita on Delilah's side of the family.
All the kids' names also start with "D", creating alliteration with the family surname Dalmatian. The parents go to work while the oldest siblings, Dylan and Dolly take care of the other siblings (the comic reliefs of the show).
The Japanese version of the show changes the backstory and expands it; before the two met, Delilah and Doug had fifteen puppies each, from previous relationships, including Dylan and Dolly; then the two got together, they then had another fifteen puppies, before then adopting 54 more, be it from rescue shelters or by taking in strays. This version being more similar to the original movie as the other 84 were adopted after being rescued from Cruella De Vil.
The creators stated that the characters of the original movie are in the official canon of the series. They are only mentioned as part of the backstory.