You should replace the “example.com” site in the django admin with the main domain name of your LMS / Open edX instance. Instead of deleting it, I recommend just editing it to change the URL/domain from “example.com” to whatever your LMS domain is.
If you very recently added your domain as a second separate “site” I would recommend deleting that second entry and then editing the existing example.com entry (it’s the default and has ID 1 and is at /admin/sites/site/1/change/ ) to use your domain, just in case any entities in the system had been linked to that existing default site entry.
Securing edX for production is potentially complex and there are many things to consider. Some of the most important are making sure that the default users (firstname.lastname@example.org) are not active, and that you are using the latest supported version of Open edX and regularly applying security updates. But in general I would recommend using a hosted offering of Open edX or contracting a company or individual with Open edX expertise to provide such support.