You say the mail server is going to be sending to the internet. That means it's going to connect to public mail servers, and the first thing it will do (as part of the SMTP HELO) is declare its own FQDN.
If you use a false or non-resolving FQDN here, a lot of mail servers are going to refuse to talk to you any further, or will use that as a strong indicator for spam even if they accept your email. You are strongly advised to register a domain name and declare a valid hostname under that, to use in the
sendmail config. If you already have a domain name, you can declare a new subdomain, and a hostname under that for this server.
The only mail servers that can get away with nonexistent FQDNs are those which are purely internal, and even then it's often so painful that I advise people to use a valid FQDN.