Taras,
Are you entirely clear on the American Fraternity system? That's not a question designed to be at all insulting, but several European countries have "Greek" systems that differ considerably from the American one (Germany in particular).
Several of the former USSR countries near the Baltic (Latvia, Lithuania, Estonia) have such systems.
I don't know that most of these European systems are really "recognized" by the American Fraternity & Sorority Life system. There's nothing wrong with them--they just operate differently and have different governing bodies.
For a new organization, it's no different from creating any other student organization at your school (college, university, high school, or any place really).
Our fraternities and sororities, generally, started like this:
-Group of people with common ideals & goals
-Create organization
-Expand organization
The Greek letters in our organizations mostly stand for secret Greek mottoes that define the goals or purpose of the organization. Greek and Latin were both languages many scholars knew--so that's mainly why they were used.
After that, the organization can do whatever you want it to. Songs, crests, pins, a new member process, a recruitment process, creeds, handshakes, symbols...whatever else you want.
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