Mac incorrectly identifying external hdd

Recently I have noticed when connecting any usb storage device (small stick or external HDD) that on the desk top and finder they all are called the same thing, that is the name of an old HDD I'm using to store media, rather than the actual name of the device.

However within Disk utility they are identified correctly by their correct name / what they are.

So, currently I am trying to back up my mac with time machine, but because the 'desk top' (and maybe the mac?) thinks the connected external HDD isn't my designated backup drive by rather my media drive, I can't back up.

This issue could have been due to have the media drive been connected and then either my mac slept for a while and powered down the drive or maybe even the mac ran out of battery while it was still connected - thus creating this issue.

Up until recently I have not have any issues with any external HDD connecting or being identified with my mac.

The media drive in question is: WD P/N: WD5000MES - 00

And here are my Mac details.

Thank you