I have hav an organization, or a site or stuff and i want to have its key name copyrighted so its not used on any other website, company, organization etc (not those who were made before my name is copyrighted), how is it done?
You don't copyright names, you trademark them. Common law trademark rights can be established upon first usage without any filing, provided the mark is able to be trademarked. You can also file for a Federal registration by filing and paying a fee to the USPTO. Trademarks are granted by classification. If there are other people who were using the term prior to you and in the same classification (same type of use) then you would not have first usage rights and they could actually stop you from using the mark.