For the life of me I can’t see how to change the names of my remote cloud devices. I see how to change the mycloud device itself, but not the connected remote devices.
It depends on the device, not the My Cloud.
You’ll need to change the name on the mobile device itself.
For iOS devices: http://support.apple.com/kb/ht3965
Not sure about Android.
After changing the name, you may need to de-authorize the device and re-register it.