Let's agree that we're not talking about the English word "geography", but the Greek word geographia.

Given that, the answer is: neither. The word geographia existed before Eratosthenes. Its earliest attestation is as the title of a work by Democritus.

If we also agree that we're not talking about Eratosthenes or Democritus, but whoever actually invented the word, even then I don't get what distinction you're trying to draw. What's the difference between coining a word, and coining a word by putting two elements together? Whatever it is you're specifically after, I guess the answer is that it's a combination of two elements: geo- is an Ionian form of the standard word for "earth", ge, so the word means "account of the earth".

Ionic was Democritus' native dialect (it was not Eratosthenes' dialect!), so it could be that it's actually him that coined the word. It's not quite decisive, though: there are plenty of other earlier Ionian thinkers who might also have thought it up.