My setup currently consists of a unmanaged server to run my site, databases, and more. I'd like to buy a separate email host such as one of GoDaddy's plans to send out my XenForo forum emails. How can I do this so the smtp information I enter in XenForo sends the emails from <name>@<mydomain.com>? As far as I can see, I just have to enter the third party service's smtp information but where's the link to my domain that makes it @<mydomain.com>? I'm really confused and want to make sure I know everything before buying.
It's possible, but you'd have to know which record is for which. Something I do not have knowledge in. However, some off-site services either give you 'A records' info for you to fill to use the domain for a specific reason. For example, to use a domain name on a blog service such as Tumblr, you need this A record info. So, look for a service you're comfortable putting your e-mails with, look for instructions - and you should be on your way.
Just bought an email plan from GoDaddy and it was way more simple than I thought it would be. All I had to do was change my MX records to GoDaddy's in afraid.org and put GoDaddy's server info into the smtp settings. The domain it's linked to is set in their control panel.