Ok I got one of these drives the other day, and I've managed to "prettify" the icon. It didn't appear in my startup items, so that wasn't going to work...
In your startup drive, go to Library/Application Support/Western Digital/WDDriveManager
Right/Control-click on WDDriveManagerStatusMenu, and select "Show Package Contents"
In the new window that opens, navigate down to Contents/Resources.
Open both WDLogoBlue1.tiff and WDlogoBlue2.tiff in Graphic Converter or some equivalent.
Convert them to 256 Grayscale, then add Alpha Channel, and erase the nasty black bit that's appeared on the left-hand side. Save these files with the same file-name as before somewhere like the desktop. Beware that Graphic Converter will try to lop one of the "f"s off the end of the name for you. The program should at this point tell you that you can't save a 256 grayscale image with an alpha channel, and hopefully will give you the option to save as a colour icon instead. Agree to this proposal.
Now drag the two files from the desktop back into the folder where the originals are. You'll be told you can't do that - click "Authenticate", and type in your admin password.
Relog.
Done.
If you don't want the menubar icon at all, you could always try just deleting the icon files altogether and see what happens. I didn't try this. If it all goes pear-shaped, you can just reinstall.