When you are using the Roku Mobile App, or are using Screen Mirroring, your Roku devices will appear in the list of available Devices as something like "Roku - 681" or something similar, as seen below:
(Android screen shown. Other devices may differ)
If you have a few Roku devices in your home, like the picture above, this can get a bit confusing.
If you'd like to rename your Roku device so it shows up in your network with the name you choose, simply sign into your Roku account at my.roku.com.
On your Account page, scroll down "My Linked Devices", and click "Rename" next to the linked Roku device you'd like to rename.
After you've renamed your Roku device, it will show up in your list of available devices with the name you chose, making it much easier to identify: