Nature names sit well on animals for an obvious reason: they are concrete. Willow, Storm, Pebble, Juniper — each of them a thing you can see, which is more than most naming fashions manage.
Flowers have their own list
Plant names are numerous enough to separate out, and the flower tag records which plant, so it can be 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.