So, I am hosting a couple of domains. And I create CNAME DNS entries to make it easy for folks to get to my server:

zimbra.<domain1>.com -> myserver.com
zimbra.<domain2>.com -> myserver.com

So, the problem I have is that whenI send email using a client like thunderbird, and I am setup to send mail using the SMTP server zimbra.<domain1>.com it correctly responds that the certificate I am using is actually for myserver.com

Can I just create and install additional certificates for these other names?