You can check the records associated with your registered domain name at
www.dnsstuff.comOnce there, enter your domain name in the Hostnames Test > DNS Lookup box at the top right of their page. Enter you hostname as mydomain.com and select All(Any) from the drop down menu. This will produce a list of all records associated with your domain name.
One of those records should have a type MX (Mail eXchange) and it should read a domain in the format "hostname.mydomain.com". Farther down the list, you should see "hostname.mydomain.com" with an A record which has your server's external IP beside it (assuming your mail server is to receive the email directly.)
All of your mail can be addressed to user@mydomain.com, but you must first ensure that you have an MX record for mydomain.com and that the MX record is set to the external IP of your server. This will tell the internet at large which IP to send email data to.
In my instance, my MX record points to mail.mydomain.com, and mail.mydomain.com points to 216.75.xxx.xxx. I can send mail to user@mydomain.com and when the sending mail server routes, it looks for an MX record for mydomain.com, which will be mail.mydomain.com. It then forwards the mail to the IP associated with mail.mydomain.com, regardless of the hostname of the server which is at that IP. The hostname of the server isn't quite relevant as long as your MX records are set properly.
I'm hoping this is helpful without being overwhelming. I know it was a lot for me to grasp when I started at this 2 years ago as I was very green coming into things - one of the reasons I like SME server so much.
If you want specific help with your domain, you can always private message me and we can work with actual values to see how things line up.