I gave mine the Time Machine icon and called it time machine. I partitioned my 1TB Western Digital External box into 800 and 200GB partitions. The 200 is my Time Machine partition. I just wish there was a way to launch Time Machine by double clicking the drive's icon. I don't like having a ton of icons in the dock either.
Mine is called Blue because when I got it I was asked to give it a name and i looked at it. It has a big blue ring around the power button so I named it that.
My HD is called Hard Disk.
But in a few days when I am done migrating files I will take them off my desktop so it wont really matter what they are called.