In slang, "a rabbit" is derogatory for a homosexual. So you don't want any of those laughing connotations behind your back (pardon the pun).
李月 sounds too much like a girl's name. You have to consider the language's cultural background to have a good name. You just can't take whatever you wished to have. You will just become the butt of the jokes.
The first thing that came to my mind of your wish list was, 李獅名 -- Renowned lion of the Li family or Lion's Name of the Li family. However, this sounds too close to 李世民, the 2nd Tang Dynasty Emperor, famous for his great administration of the country but at the same time, he killed his older brother to gain the throne and forced his father to abdicate.
If you wanted a transliteration of Leonardo, there are many ways but you have to consider the meaning taken as a combination of characters as well. The best one I came up with is 李納道 "Embracer of Taoism" and the Lao Tzu, the founder's last name is also 李.