The VPOP3 Host Name is used by VPOP3 when it is telling other mail software what it is called. For instance, when it connects to another SMTP server it will send the host name as the parameter for the HELO or EHLO command, and when an SMTP client connects to VPOP3, it announces its name in the welcome banner as required by the SMTP standard.

In many cases you can just specify a name which looks like a valid host name - e.g. mail.<your domain> (mail.company.com). It is rare for ISP SMTP relay servers to check this because they use more reliable forms of authentication. (Note that the SMTP standards strictly prohibit the receiving mail server from blocking mail if the host name is set incorrectly).

It is best to use the actual Internet host name of your mail server and have a reverse DNS value set up pointing to your IP address with that same name in it, but this is usually only useful if you have VPOP3 sending outgoing mail using MX routing. However, this may not be possible in many cases (for instance, if you have a dynamic IP address or don't own your own domain), so in those cases just using something that “looks” like a host name will probably work.

It is not necessary for the VPOP3 host name to bear any relationship to the email addresses being sent out from that copy of VPOP3, but in many cases they will be in the same domain.