How do I find out who my domain provider is?

Who do you pay for hosting? That’s who your hosting company is. The same with the domain name. They might be the same company, or different companies, so you should go back through your bills to see who you’ve paid for these in the past.

Apart from that there’s always a webiste like http://www.whoishostingthis.com/ that will tell you the main comapny that’s hosting the site. You can also get the domain registrars name from a WHOIS on your domain name. Neither of thse are perfect though, as they only tell you the top-level companies, and not which ever resellers that you’ve purchased from.

You have a login account at https://wordpress.com/, and there is where you can find your site and access it to do whatever you can do there. These wordpress.org forums are for wordpress.org support, and your support for everything related to your site and wordpress.com can be found at https://en.support.wordpress.com/.

I’m trying to get this information to convert to the fully hosted .org.

Okay, now things are more clear.

wordpress.org does not host any sites, so your first matter of business is to select a host and set up an account there…
https://wordpress.org/hosting/
There are many others also, and nobody here at these forums will recommend any over another.

After you have hosting somewhere, you would use your wordpress.com Dashboard to re-point your domain to the new nameservers if there is where it is registered…and there is no need to also transfer your domain registration to any different Registrar unless that might just be something you want to do anyway.