My Shared network is breeding Mac minis...

A belated reply, sorry: turning off the Wake for Network Access makes no difference. I STILL have 23 numbered icons of my Mac mini in the Shared section of the Finder sidebar. I've run through all the diagnostics I can think of: disconnected all of the mini's HDMI, USB and power cables, shut off its WiFi, reconnected and restarted everything, I've zapped the PRAM and restarted in Safe mode, I've rebooted my Verizon FIOS router, and found normal connectivity between the router and the Mini on the home network. If there are other troubleshoots out there for this problem, I'd love to know about them. Thing is, there doesn't appear to be any significant impact on performance, at least that I can detect. It's just that seeing 23 extra versions of your desktop device showing up in the network is just WEIRD. Has anyone else ever experienced this phenomenon, or is it....(gulp)...just ME?

Thanks for the advice. Hadn't heard about a possible Yosemite bug till now. Renaming sounds like an interesting fix; there are no special characters or punctuation in my device's current name. VerizonFIOS failed through remote troubleshooting to find anything wrong with the router and essentially blew off the notion that there's anything wrong with the VerizonFIOS equipment.