The capitalization (EOS) is only used by block.one to identify the call letters for the token. The name of the software (written by block.one) does not follow this capitalization rule, and can be seen on their website written in all lower case, all upper case, and with just the E capitalized.
Following the news and constantly viewing the website (eos.io) shows that the name was chosen because of the greek mythology name. The pictures and process of introducing the token hint at this, as does the name for their updates of progress (Dawn 1.0, ... Dawn 4.0) But officially, a statement from their CTO Dan Larimer says the name can be interpreted however one wants, and is not a specific initialism or acronym for anything.
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This makes complete sense to me. perfect explanation esp. the connection between the releases named Dawn 1.0 etc. I had totally missed to connect this with eos. Thank you for your insights on it!