Pretty silly thing to do really – I have left the default site name when installing SRM 5.8 so it has FQDN of my vCenter box instead of a proper name:
From vSphere Web Client point of view having FQDN in there is not ideal as well as introducing confusion which site is which (live vs. recovery):
To get the site name changed we need to edit vmware-dr.xml which lives (by default) in the following location:
C:\Program Files\VMware\VMware vCenter Site Recovery Manager\config
From there its just a matter of editing the .xml and changing the displayName value to something meaningful:
Restarting vmware-dr service (VMware vCenter Site Recovery Manager Server) should be all it’s needed to have the name changed.