Count the names in these registers by length and two syllables wins by a distance: more names sit there than at one and three combined. There is a reason. One syllable arrives fast but clips; three gets shortened by the owner within a fortnight. Two survives both.
Counted, not estimated
The syllable count comes from the vowel groups in the spelling, with silent endings handled, so it agrees with how the name is said rather than how it looks. Getting that wrong the first time cost this catalogue a thousand incorrect counts, which is why it is worth saying it is now checked.
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.