mv is indeed the command to move files, but the inner workings of mv also makes this the 'rename' command.
mv file01 file02 => first copy file01 to file02 and then, after this is done succesfulley, remove the original (file01 in this example).
See man mv for more details.
PS: There's also a rename command in linux, but this does _not_ do what you expect (man rename for details).
Hope this clears things up.