Hi @annette2. We suggest that you request the license file with the information that is listed in hostid.txt. This can be access via Start menu > FlexNet for Safe Software > Generate hostid.txt. This will generate hostid.txt in the folder where you've installed FlexLM.
Once you've checked this and requested the license file, on a client machine using FME Licensing Assistant, you should be able to enter the desired CNAME as long as it resolves into an IP address. As long as it resolves into an IP address it should connect to the license service.
Let us know how this goes!