Anastasia, Bartholomew, Persephone. Long names are the ones people fall for and then stop using: within two weeks almost every three-syllable name has a two-syllable form that the animal actually learns. That is worth knowing before you choose, not after — the short names hub is the other side of this argument.
Choose the short form deliberately
If you want a long name, pick its abbreviation yourself rather than letting the household invent three competing ones. The animal learns whichever it hears most, and a name being learned twice is a name being learned badly.
Are long pet names a bad idea?
Not bad, but they are usually shortened in practice. If you choose one, decide its short form deliberately, because the animal learns the version it hears most often.
How many syllables is best?
Two is what the registers overwhelmingly contain: more names sit at two syllables than at one and three combined. That is what owners choose, not a rule anybody imposed.
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. Browse the whole catalogue or read how the data is put together.