Most lists of unisex pet names are a list of names somebody felt were neutral. This one is a measurement: a name is unisex here when the animals carrying it were sexed between 35% and 65% female across a sample of five or more shelter records. Nothing was chosen for sounding androgynous.
The names that surprised the data
Some names read as strongly gendered and measure otherwise, and some do the reverse. That is the value of counting rather than assuming: Charlie and Riley are used across the board, while names that feel neutral often turn out to sit firmly on one side once the records are counted.
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.