Screen Share connects to wrong device I have a Mac mini (Mac mini 2) set up in New York which I can connect to just fine via the Share Screen... button on Finder. However, when I try to connect to my other Mac mini in Miami (Mac mini 3), it says Connecting to Mac mini 3... then shows the screen for Mac mini 2. What's going on? I am able to successfully SSH into both.
Bonjour can mess up machine names.

I would use ssh or ARD to set the host names to be different. 

sudo systemsetup -setlocalsubnetname pear


(Or in ARD, you can specify that without the sudo but to run as root)

If you need more help, you'll need to ask a follow on question explaining how you have things set up. Is iCloud back to my mac the service for locating the remote IP address?

If so, you can browse things from terminal:

 dns-sd -B _ssh


Look for remote machines to be like

12:27:50.451  Add        2   0 12345789.members.btmm.icloud.com. _ssh._tcp.           mini-3


Changing the registration for each Mac so that it's names of fruit, for instance would make it easier to know if you are connecting to apples or oranges.