> why would a galactic spanning organisation be called "Galactic Federation"?

We called the earth beneath our feet "Earth". Our moon "Moon", our star ("our sun" in common language) "Sun". Our military has a force that deals with flying in the air and we called it "Air Force". Our first space force is called "Space Force". Historically, one of the biggest companies that dealt with the east indian area was called "East India Company" despite being British.

So, I'd answer back with "why not"?