I was not able to add the internal name since the certificate comon name is mydomain.com, so to add the alternate name servername.mydomain.local was not possible on the same certificate.
OR is it possible?
Godaddy is the one issuing the UCC certificate.
For alternate names I have:mail and autodiscovery so I end up with mail.mydomain.com and autodiscovery.mydomain.com
I did created a primary zone on my internal DNS with mydomain.com and added the record for autodiscovery and mail.
What is your opinion?