Certificates for exchange server in child domains

Hi Team,

We have 2 child domains on which Exchange 2013 is installed. We have issued a single SSL certificate from our internal ADCA server in Parent domain.
This certificate is installed on the exchange server in child domains.
THE SAN name has all the url's required for autodiscover and OWA access.
When we try to open OWA url for both the child domains we are getting the certificate error as the CN name on the certificate is not the same as FQDN of any of the CAS servers.

Do we need to generate 2 certificates from ADCA with different CN name (Same as FQDN used to access CAS server from outside network) to resolve this error?

Thanks,

Mitesh Jain