(I mean, Usagi isn't a normal Japanese name,
is it?) 

I don't know how representative this is, but a friend has gotten me
addicted to a Japanese soap opera that some tiny station here in the NY/NJ
area is broadcasting subtitled, and the female lead character, a young
Office Lady type, is nicknamed "Usagi"; none of the other characters seem
to think it an odd or unusual name.

-- Bob