I'm a little confused by your "spans the nation" description, too. Do you mean you all come from different places but are together in one place now? Or do you mean that you are close friends with people who currently live in different places across the country? That second scenario does not lend itself well to the formation of a new sorority that will last.
I don't think it's necessary to pin the OP to the wall about why this group wants to evolve from a group of friends to a group of sisters. And suggesting they joing a service club instead does not address her original question.
To the OP: No, there is not central entity with whom you must register. Try to select a Greek letter name combination that has meaning to you but is not in use by another org. (Good luck with that. It will be tough.) Unfortunately, there is no recipe for creating traditions, symbols, and rituals. Start with just the bare bones and let the rest develop over time. You are no more or less legitimate if you have a simple structure. These things don't define the strength of your sisterhood bonds --- that comes from your love and respect for each other.
One thing to consider, though.... Since the girls who want to create this new organization are already so tight, how will it change the group dynamic to bring in new members? This might be your biggest challenge. Your group might seem cliquish to a PNM looking in from the outside.
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