Are MX record names important? [closed]

The owner name is crucially important as it has to match the right-hand-side of the email address.

Eg [email protected] -> look up example.com MX, [email protected] -> look up bar.example.com MX.

If the MX exists at mx1.example.com it will only serve any purpose for mail sent to addresses ending with @mx1.example.com (which I'm guessing is not the intention to have).

As for @, this is a special value in the "master file format" (standardized plain text representation of DNS data) which is a shortcut for "current origin".
What you need to focus on is that you want to add an MX at example.com. (presumably), not how one might achieve that in some different system than what you are dealing with. If you are working with a GUI, it will come down to how that interface was designed to work. If it's not sufficiently intuitive that you can work out how to do it, you would have to consult the documentation for this specific interface.

You can also give the name for MX record as domainname.com. (the period character at the end is required), replace with your primary domain hosted in CPanel.