-y and -ie are the sound of English affection: they take a name and make it smaller and warmer, which is exactly what people want from an animal's name. Charlie, Rosie, Benny, Millie.
Why the ending is recorded, not guessed
The site classifies how a name ends from its spelling — y, ie, a, o, i, s or other — which makes this a fact about the name rather than a category somebody sorted by hand. The same field powers the search page's Ends with control.
The trade-off
An affectionate ending also softens a name, and a soft name is harder to make sound like a recall cue. If you are training in a busy place, pair it with a short, harder-edged nickname for work.
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.