A name sounds playful for reasons in the letters: repeated syllables, open vowels, a soft ending that lifts rather than stops. Bobo, Peppa, Zuzu. The site computes this from the spelling, which is the only way to filter on it honestly.
What the tag does not claim
Nothing about the dog. A playful-sounding name on a serious dog is a joke that works; the classification describes how a name behaves in the mouth, not how an animal behaves in the house. There is no source anywhere that connects the two, so the site does not pretend there is.
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.