Renaming of mapped drives on a per-user basis is easily done through right-clicking it and choosing Rename. What if you wish to rename the share for all users on a network?

Create a VBS script in the NETLOGON share:

mDrive = "N:\\"
Set oShell = CreateObject("Shell.Application")
oShell.NameSpace(mDrive).Self.Name = "New drive name here"

Replace N:\\ with the appropriate drive name, save it as renamedrive.vbs for instance.

Next, add the following line to the login script:

wscript //b renamedrive.vbs