Subscription name is getting from Service template (exactly service template name). Subscription name doesn't contain domain name.
POA API version 5 will set service template name as subscription name in POA.
Consider using API version 6 if you want to have domain name in subscription name. In API version 6, the subscription will get the name as 'service plan name (domain name)'.
Service plan name - Linux Shared Hosting
Domain name - testdomain.com
Subscription name will be - Linux Shared Hosting (testdomain.com) both in POA and PBA.
Please note that POA API version 5 is deprecated in PA 5.5 .