The user will need to be granted to the new service domain with the appropriate rights. To do so:
a) After you created the new service domain, exit and log back into Stat
b) Go to Maintenance | Security Settings | User Maintenance | double click on the user | click on the Service Domain Access tab | New and grant the new service domain to the user
c) Go to Maintenance | Domain Specific | Work Queue | Queue Assignments and grant the user access to the queue otherwise you would not see this user name in the queue when creating a new csr.