Impact of changing hostname on postfix and other software?

I'm running postfix, dovecot, apache, php, mysql etc on Ubuntu 12.04 and (I think) I now need to reset my hostname and regenerate my smtpd.cert SSL certificate so that my certificate is validated by email clients. At the moment, Thunderbird launches a warning dialog saying "Wrong site: Certificate belongs to a different site" and prompting user to cancel or create a security exception.

So, I guess I need to change hostname to reflect my primary domain, then generate a new SSL cert with those same details.

Is this correct, and what other unforeseen impacts could changing the hostname have?

From what I could find, I need to change hostname in "/etc/hostname" and "/etc/hosts", then "sudo service hostname restart" and also change hostname for postfix in "/etc/mailname"

Anywhere else?