Thanks for the replies.
1 I have now renamed the internal hard drive as "Macintosh HD" and that seems to have worked OK.
2 The rules for back up with several different users on the iMac seem to be as follows:
If user A backs up all the user folders for users A,B,C,D using Finder to drag & drop or copy/paste to the LaCie external hard drive, then only the user A folder is accessible, and it is only accessible to user A.
The folders from users B,C,D are NOT copied on to the LaCie and cannot be accessed there even by users B,C,D.
If user A backs up all the user folders for users A,B,C,D using CarbonCopyCloner to the LaCie external hard drive, then all the user folders for users A,B,C,D get copied across.
But only user A can access the user A folder.
And only user B can access the user B folder.
And so on.
That makes sense and seems secure.
But if you use only FINDER and not, for example CCC, then each user must log in and copy across his own backup material to the external drive.
3 One other weak spot I have noticed when backing up photos from iPhoto is that many of the apparently OK photos on the external hard drive are just 4KB Aliases and cannot be opened, as the originals cannot be found.
I don't claim to know why that is exactly, but as a warning, it is good practice to check the size of folders before and after copying.
And try opening a good number of apparently OK backup copies - this is the acid test.
All the above is just based on my own recent experience with OSX 10.2.8 and iPhoto 2.0.1 on a G4 iMac - others may have different views.