I have had a few questions recently around changing the Connection Broker DNS name (alias).
This is simple to do and can be achieved by two simple steps:Firstly, you will need to set the active connection broker by going to RDMS, Overview, Deployment Overview, Tasks and set active RD Connection broker.
Then you will need to run the Set-RDClientAccessName PowerShell cmdlet
Set-RDClientAccessName -ConnectionBroker "RDCB.company.com" -ClientAccessName "RemoteResources.Company.com"
For more info on changing the RDCB DNS Alias, please see the following TechNet article.