Catch 22: I just found this thread while trying to solve my own Global Host Name problem. I'm getting the GHN/Bonjour prompt when I try to assign static DHCP reservations to two Airport Express units on my network, which ARE running Airport Utility firmware v7.6.3. Unfortunately, my main Time Capsule router only can run firmware v7.6.1.
Why? Before this latest Global Host Name issue came up, I had to install a new Netgear GS724Tv3 gigabit switch on my network. After upgrading all my Airports and Time Capsules to the v7.6.3 firmware updatea a few weeks ago, my old Netgear GS724Tv2 switch died (power supply wouldn't power back on). So, I bought Netgear's newest v3 model as a replacement switch.
Unfortunately, I then learned that Apple's v7.6.3 firmware update may have a nasty bug making it incompatible with the new Netgear switch (or maybe new firmware in the new Netgear switch is the bug). No matter: every time I connect the v7.6.3 Time Capsule to the Ethernet network via the new switch, the Ethernet network dies and devices cannot see one another. Stepping back my main Time Capsule router to firmware v7.6.1 resolves the problem, but apparently, if I correctly understand this thread, the v7.6.1 firmware now may be a factor in preventing the establishment of a Global Host Name, which I'm being prompted to do when attempting to set up static IP addresses for the other Apple devices.
Now maybe I can sidestep this issue if I drop back to firmware v7.6.1 on all my Apple Airport gear (everything was upgraded to v7.6.3 all at once, and after encountering the networking bug, I only downgraded the main router, since this action immediately solved by Ethernet problem. I stopped the troublshooting — until now). Alternatively, I could replace the two other Netgear switches on our network plus two new Time Capsule's and three Airport Express units and hope those actions solve my networking problems.
What a mess. None of these devices are more than four-years-old.
Catch 22 author Joseph Heller needs to write a new novel – about the dysfunctional madness of computers.