Hi and welcome to LinuxQuestions!
It's not really clear what do you refer as "label name". You can change the label of a partition independently from its mount point. You have only to take care that the change is reflected in /etc/fstab if it uses partition LABELs. Anyway, please post the output of fdisk -l (as root) and cat /etc/fstab, then please show us exactly what do you want to change. If the partition is formatted as ext2/3/4 the command e2label may come in handy.
Please note that I pruned this post from the ancient thread you submitted to and moved it to Linux - General since this is not actually a Hardware question.