Server Name Local vs Public

I recently installed Spark on our SBS server. I set the server name to be the local DNS name of the server. I am having no issue conencting Spark clients that are on the local network or over a VPN. I would like to use a public DNS name to the same server so that clients such as mobile phones or offsite users do not need to use the VPN. If I create a public name such and open all of the relevant on the external firewall is there any configuration changes I would need to make on the server? I am imaging that for Spark clients the server on the login page would be the local dns name and under advanced the host would be the public domain? Is this correct?

Thanks in Advance.