Hi SMP,
Using the hostname command won't update the BIG-IP-specific configuration for the hostname. From SOL4802:
https://support.f5.com/kb/en-us/solutions/public/4000/800/sol4802.html
For BIG-IP versions 9.4.2 and later:
bigpipe system hostname
Replace with the fully qualified hostname for the BIG-IP system.
For example:
bigpipe system hostname askbig9n1.askf5.com
For BIG-IP versions 9.0 through 9.4.1:
bigpipe db HostName
Replace with the fully qualified hostname for the BIG-IP system.
For example:
bigpipe db HostName askbig9n1.askf5.com
Maybe someone else can comment on any changes you'd need to make for the GTM's.
Aaron