Sorry it took me so long to come back to you.
I found that a few years ago a pet insurance company made a survey and listed the most popular name for bunnies (top 10):
1. Momo
2. Maron (came from French "marron" = chestnut)
3. Choko (came from English "chocolate")
4. Hana (maybe from western name "Hannah")
5. Mimi (Western name but it also have a meaning "ear(s)" in Japanese)
6. Koko (maybe from Coco, like Coco Chanel)
7. Moko (most likely from onomatopoeia "mokomoko" means soft and fluffy)
8. Purin (came from English "pudding")
9. Sakura (cherry blossom)
Miruku (=milk)
Moka (came from mocha, type of coffee)
Rin
10. Nana (can be either Japanese female name or western name)
Rabi (from English "rabbit")
As your bunny is brown, you might name him
Maron
Choko
Moka
Or alternatively, something common for rabbits such as
Mimi (too feminine?)
Pyon (from onomatopoeia "pyonpyon" describing something small like rabbits hopping and jumping) or its variants
Pyonta
Pyonsuke
Pyonkichi
(-ta, -suke, -kichi are common extention for name's name. -suke and -kichi are not used for people these days but still can be seen for pets' name)
I personally like
Usakichi (usa = usagi meaning "rabbit") + -kichi (same as the above)
for male bunny.
Hope you'll find something satisfactory among those I listed for your cute bunny!
