To find the label of the partition,
type in
Replace the * with the appropriate device letter and partition number
No, Linux is still going to use /dev/hd* (or /dev/sd*)
But some distros, like Fedora have switched from using /dev/hd* to using /dev/sd* for all PATA/SATA drives. If your grub references the devices by that name, you wouldn't be able to boot.
You can even mount partitions by their label, example mount LABEL=/home /home would work (provided you have a partition on your system labeled '/home')