You can name a rabbit anything you like. Also, if you put some effort in you can train your rabbit to come when you call so you may want something short. Sorry but Miss Floppers Pookey Honey Bun Cutie the Third isn't going to work. Although, if you don't want to train them you can go with whatever name you want- even if it does leave you winded. ;-)
The rabbit in The Velveteen Rabbit is just called "Rabbit"; it has no other name.
the name of a rabbit's offspring is jumbalia
In the movie Bambi the rabbit's name is Thumper. Thumper is the grey rabbit that is Bambi's best friend.
The rabbit on the Magic Roundabout is named Dylan.
The name of the rabbit is Harvey.
Boingo was the name of the rabbit from Hoodwinked!.
The scientific name for the domestic rabbit is Oryctolagus cuniculus.
The scientific name for the European Rabbit is Oryctolagus cuniculus.
Snowshoe Rabbit.
gray rabbit
Another name for a male rabbit is "Buck".
the rabbit's name is Thumper if that is your question