It's "elementary" and not "Elementary".
But what about eOS?
"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 word “elementary” should be used when referring to the overarching project. “elementary OS” is a product of elementary. The “e” should always be written in lowercase. Don’t use “eOS” as an abbreviation for elementary OS; it sounds a lot like a certain fruity operating system and reminds us of the “KThis” and “GThat” trend.
Why is it necessary to avoid the K/KDE, G/Gnome, i/Intel trend?