I am not great at understanding DNS, so please have patience. I have a server set up at home which can be reached at an address similar to foo.dns.org, under a domain that I do not own but that I get to use for free. I have client software running on the server which lets the nameservers know when my IP is updated.
Aside from this "false" domain, I also have a real domain (like foo.org) that I own, and that is using nameservers that are supplied by the company where I bought the domain from.
Using the domains for simple "foo.org -> IP" resolution seems to be no problem, that is what I am already doing with the free foo.dns.org variant that I have. But here is my question:
Is it possible to use either of these as my "actual" domain when connecting to other computers on the internet? Could I connect to IRC and be seen as actually "being" foo.dns.org or foo.org, instead of whatever identity I get assigned to by my ISP? Hitting my home router when you type in "foo.dns.org" seems to be an easy task, but actually being identified by that name (or even a paid domain) out on the Internet seems impossible.
I am suspecting that I am unable to do this and the reason is that my ISP (and private ISPs in general) does not allow it, much like SMTP servers are not allowed on private connections, but I am interested in knowing what terms I should look for and read up on to understand why this is.
Hopefully my question makes sense, thank you in advance for any pointers.