I have some problems importing my music files in Rhythmbox.
Under Preferences -> Music I set the directory hierarchy I want but when I import music from a directory it doesn't copy the files in my music dir. Also if I manually copy the files in my music it imports them but doesn't rename them.
Rhythmbox is a music player that allows easy browsing and searching of your music. Audio files (.ogg, .mp3 etc.) have a feature called tags. Tags are small pieces of text that describe the audio file they are in. Examples of tag types are: 'album', 'artist' and 'genre'.
When you import files into your library, Rhythmbox extracts these tags, as well as the location of the file, into its database. It then uses the database to provide the interface that you can use to browse, search and play music. It also allows you to edit the tags in files. Tags replace the semantics of the underlying file hierarchy.
Your default music location is there for when you rip CDs. CDs don't contain tag information so Rhythmbox looks them up online and then uses your preferences to create the music files on your disk with your preferred naming scheme.
If you don't like the way Rhythmbox works, you can install other music players from Ubuntu Software Centre:
As you can see, there is plenty of choice.
About not copying or moving the files, I think this is just how Rhythmbox works (and I prefer it that way, personally, but I know other people prefer it differently).
I'm not sure what you mean by rename; do you mean automatically rename all files using the filename template based on the tags? (And I would be really upset if any music manager would rename files without my express permission--this could break other applications--but again, tastes differ ;) ).
If Rhythmbox doesn't work like you want, you can also try alternative music managers. E.g. Banshee is quite popular, and also has a U1MS-plugin if you want to have that, but there are others too.