Something important to elementary and for elementary OS is our branding. For a quick reference:
"elementary" is the name of the company. It is never capitalized. Refer to "elementary" when you're talking about the company itself or the developers. Think of "elementary" as the group of people.
"elementary OS" is the name of an elementary product. "OS" should be capitalized as it stands for "operating system". The company name is still not capitalized. There is a space between the company name and the product name. When referring to the product, always use "elementary OS" and not "elementary".
"eos" is the name of a line of beauty products or Canon cameras. We don't consider this an acceptable way to refer to elementary OS. This is especially important in not encouraging 3rd parties to make brands such as "eRadio" or "eCleaner".
The lowercase "elementary" is confusing to readers since Elementary OS is a proper noun. Readers use capitalized letters to distinguish unique entities from common text. Journalists who write about the OS use style guides that will automatically capitalize Elementary for this reason: readability. (See the Wikipedia article to see how much easier it is to read mid-sentence.) It's fine to have "elementary" lowercase for branding materials and PR documents, but there's a reason why writers will not use the stylization so let's not enforce counter to that, especially on tech support questions.
"elementary OS" is long. I get the anti-"eOS" rationale but then what is the alternative? (Something like e9os, a numeronym like l10n, might be a useful shorthand here and would make search easier.)
The urge to standardize can be desirable but I don't see how it would be for the best in this case.
e, as I have with a few by now) there's not much that can be done.