How to rename an external hard drive in Mac OS X?

I have 2 external hard drives supplied by the same vendor.
They both have the same name.
Using them with the mac is problematic when they have the same name.
Time Machine, for example, tries to back up to the external drive with this name.
I would like to simply change the name of one of these external hard drives.

Multiple forums have suggested 2 solutions:
1: In Finder, just change the name of the drive like you would any folder
2: Use Disk Utility

Neither of these solutions work for me.
The name of the external drive is read only in both applications.

Solution 1:

If the file format of the external hard drive is NTFS, then El Capitan will allow you to only read the contents of the drive. To rename the drive, or to modify any contents of the drive, you will have to format the drive with OS X File system.

Solution 2:

I was having the same issue with wanting to change the name of my external hard drives. What I found is my Mac did not want to change the name. So I plugged the drives into my PC pulled them up on Windows Explorer, right clicked on the drive name picked "rename" and typed in the new name. It changed with no issues. I plugged the drives back into my Mac and ta-da, the name was changed.

I did not need to change the format.