How do you manually reposition faces in Mac OS X Yosemite's Photos App?
This answer in the Apple Discussions/Communities suggests that this behavior (inability to move the naming circle) is a bug in Photos; to remedy it requires restarting the Photos app (which may not be as easy as just quitting and then double-clicking the app icon, perhaps requiring a system reboot).

After just experiencing this problem with Photos version 1.5 running on El Capitan (MacOS 10.11.6), rebooting worked to clear it for me.