Naming a dog after a character is a small act of quotation, and it helps to know what you are quoting. Every name tagged pop culture here is recorded against a specific work: Simba against The Lion King, Gizmo against Gremlins, Falkor against The NeverEnding Story.
What is deliberately not here
Ordinary given names that happen to appear on screen. Phoebe, Dexter and Bruce were removed from the tag for that reason — a name only counts as a reference when the reference is the reason people use it. Anime gets its own tag, because it is what people search for.
Every count on this site is a tally of real registrations: pet licences and shelter intakes published as open data by New York, Seattle, Austin, Montgomery County, Cambridge, Zurich, Basel and three Australian councils. Popularity here is the average share a name holds across those registers, so a name common in a small city is not buried by one common in a large one. Nine of the eleven sources are North American, so read the ordering as naming in those places rather than worldwide.