I am exporting to FBX and then importing to Blender. The meshes are all named  like this CC_Base_Body. Say my characters name is John. How do I get CC3 to name the meshes John_Body, John_R_Eye etc?

I do not think you can.
You can only add a prefix and/or postfix to mesh names, like John_CC_Base_Body or CC_Base_Body_John.
There is section for that at the FBX export panel.

Bummer