Domain Names, and web servers?

I remember once i had a web server app that allowed me to create a domain name w/o having to pay/register it. and it did work.
I am now thinking of setting up a mail and web server using a linux system. Now when i set up linux it asks me to create a domain name. now if i pick a name like www.myname.com will it host my site? I will be using Apache Web Server Project.
And if i do get it to work, …

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