How to change computer name as it shows up in AirDrop?

You can opt out of AirDrop on a Mac quite easily.

• turn off WiFi
• Use an OS X Profile to disable sharing via AirDrop (MDM such as OS X server.app's profile manager can do this easily)

Setting the name should be easy to test. Open the sharing preference pane and make one Apple an Orange. Watch that the names change. If not, you've got a caching issue with your network and might want to power off all AppleTV and Airport devices at the same time to get a clean start to that cache. I haven't figured a more elegant way to purge the collective shared cache of bonjour names that works as well as a total outage there.