It should not.
I do not have exact code to test, but in 7.0.116.0 I can change the mobility group name without any reboot.
(WLC2) >show sysinfo
Manufacturer's Name.............................. Cisco Systems Inc.
Product Name..................................... Cisco Controller
Product Version.................................. 7.0.116.0
.
.
(WLC2) >show mobility summary
Symmetric Mobility Tunneling (current) .......... Enabled
Symmetric Mobility Tunneling (after reboot) ..... Enabled
Mobility Protocol Port........................... 16666
Default Mobility Domain.......................... DMZ
.
.
WLC2) >config mobility group domain DMZ1
(WLC2) >show mobility summary
Symmetric Mobility Tunneling (current) .......... Enabled
Symmetric Mobility Tunneling (after reboot) ..... Enabled
Mobility Protocol Port........................... 16666
Default Mobility Domain.......................... DMZ1
HTH
Rasika
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