mmmhh... Not sure what you want? If you have a physical server for hosting Moodle, it will have nothing to do with your hosting company. A sub-domain would still be on THEIR servers and NOT YOUR server.
If you want to host a Moodle Server yourself you will need:
1) A fast internet connection with a fixed IP address.
2) A registered domain name for the above IP address.
4) Time to check that no one attacks or hacks your server.
Unless you have a lot of technical knowledge, it's probably not a good idea. However if you know Linux well, it is not so difficult.
Hope that helps