Yes. You will need to update the FQDN in CUCM for the MGCP gateway.
Same story goes for H.323 if the gatekeeper zones reference the DNS name: you'll need to update them. If the router you are modifying is the gatekeeper itself than any registered devices (eg gateways, MCUs, etc.) will need the new FQDN. Conversely, if the router you are registering to is a gateway that registers to a gatekeeper then you may need to update the config of the gatekeeper unless it is entirely technology-prefix based and has nothing specific to a particular gateway registrant.