Hard Drive naming, numbering and lettering

it can be a drive has several partitions ( eg Windows7)
then your boot drive would be C: and the system drive D:
however, if there was a card readerconnected during the install of the oS - these can take the 4-5 first letters

another explanantion is that if windows hides the boot drive, the system drive becomes C:
while dirsk management shows both
you have NO control over t his

Well, the only control you do have is that you can remove drive letter assingments from partitions, making them effectively invisible. That is what happens to the 100 MB system partition that Win7 creates. You can shuffle the drive letters around later on though, and usually the mappings are retained even after a reboot when set manually. The problem is that when the C: drive is assigned something else, you can't easily change this without extensive registry and config file changes.

I have a feeling though this is rapidly going off topic! ;)

The E  drive is named FWU System Backup E in Windows explorer. The same drive is named Game Backup 1 Ext E in disk management.  I have never had this happen before. There is no way you can rename a drive in disk management.  

CD Drive F shows up in Windows Explorer but not in Disk Management. In Windows Explorer the full name is CD Drive (F:) FWU Data Backup F.  The context menu in Windows Explorer does not give me the option to change its name. The icon indicates that it is a CD drive.

That looks like the caching information is somewhat messed up. You didn't say which Windows version you're using, but you could potentially run this and see if it helps:

http://www.microsoft.com/en-us/download/details.aspx?id=2648

I have also found this forum thread, it seems to correspond what you're having issues with. Have a read and see if any of the steps help you. I couldn't write it any better:

http://forums.techguy.org/windows-7/882033-solved-drive-labels-windows-explorer.html

Again, it depends which Windows version you're running. It may work for other versions, too.

it looks like at some point the same drive got another name from running another software.
can you confirm this ? (many software propose a (generic) name of their own)

I don't recall.  What would you advise?

Do you still have the CD that could have named the disc drive "FWU Data Backup F"? If so, insert it again and then eject it right after. Perhaps by using a right click on the disc drive and click on "Eject" that way. It might clear the name.

the  software - when used, often offer the possibility to save to another location, or disk
at this point the name can be changed; so yes - use the software again from the start, and see what it allows

Thank you so much for your thoughtful comments.