The meaning of the name Mulberry is “Sensuous”. Mulberry is a nature name, being that of a tree and the berry that it produces. A new age ‘hippiesque’ name that is organic and free spirited with classic roots. The nickname Molly makes it very useable.
Mulberry comes from Old English root word mōrberie, which, if you really like offbeat names, could be used with nickname Moby for short.