As you only have a single mail server that is addressed by the host name, not a domain name hosted on the machine, your customer must use the mail server name. The SSL certificiate is made out to the single mail server on your machine. It is only a server name, it is not the domain name that shows up as a "sender" in an e-mail's visible part.
Example: If your customer hosted mails on Office 365, he does not have a choice how the mail server is name either. He would get some cryptic name like business01-de.provider.tld without any discussion. It should really not be of any concern to anyone what the host name is, it is simply a technical expression that practically noone sees but tech admins that configure e-mail settings.