Is it possible to reference hard drives by their names rather than their drive letters?

Or, can I globally change the drive letters that were assigned by the system on boot up? Example: Old E:\ is now H:\ but maybe tomorrow it might be I:\ or go back to E:\ depending on what I add or remove.

Here's my problem.

All of the shortcut icons on the desktop point to the source on a particular drive using drive letters.

However, when I add (or remove) drives these letters change the next time I boot and now the shortcut icons point to the wrong drive. I don't want to go into each property of each icon and change the drive letter to the new drive letter otherwise I would be doing that all the time as I add amd remove drives.