Why does my iPhone show up as "iPhone (3)"?

This has been driving me crazy for months:

My iPhone shows up as "iPhone (3)" sometimes. I go to Settings>General>About, and change it back to iPhone. It stays OK for several hours or a day or two, and then it pops back to "iPhone (3)". Even after I've renamed it, and rebooted it, and the name sticks as iPhone, it still shows up as iPhone (3) in the WiFi listings as a hotspot for my Mac or iPad.

I've tried everything. Totally shut down every piece of Apple gear (Airport Extreme, Watch, iPhone, iPad, Mac) -- no other Apple gear is on. Turned everything off at once to clear out any cache poisoning, then turned everything back on. Same problem. Running iOS 8.4, Apple Watch 1.1, Mac OS X 10.10.4, latest AirPort software, and Apple TVs (2 of them) are completely unplugged -- not plugged back in since reboot.

Any ideas how to change it back to iPhone everywhere?