Computer showing up multiple times as "Shared"

I don't know much about how sharing thing works, but here's what's going on. AFAIK this only started after I upgraded to Yosemite.

My Mac Mini's name is "Otto" (don't ask). I'm used to seeing "Otto" show up in the "Shared" list in Finder, and my spouse sees it too, on her iMac (same wifi network).

Now both her and I see:
Otto (1)
Otto (2)
Otto (3)
Otto (4)
etc., all the way down to "Otto (14)." When I checked File Sharing in Preferences, it says my Mac Mini is now called "Otto (14)."

What? Why? And where are all those other Ottos? (Note that the other ones come and go; sometimes they're all listed, and a minute later only three of them, then eight of them, etc.)

So I went in an renamed my machine from "Otto (14)" to "Mac Mini." Now I see "Mac Mini" in the list along with the expanding and contracting list of Ottos (but "Otto (14)" is no longer listed.)

When I connect to the Ottos they all show the same thing (basically the contents of my Mac Mini). WTF is going on here, and how do I fix it without hosing my actual machine (as opposed to these ghost Ottos). Help!