Order, I say
The Loyal Order of Moose (we were looking them up as a conversation drifted from how to translate лось into whether they existed - the Order, not moose - or not) has a web page that offers multiple languages. They do that via Google Translate.
Which is too bad.
Loyal Order of Moose gets rendered in the text as Постоянные орденом лося and Постоянный орденом лося, which mean "the constant (or "unchanging") ones with the order of the moose" in plural and singular. I would think Верноподданный орден would be better, but in any case "order" ought not to be in instrumental.
However, in their navigation bar, for whatever reason, it's rendered as постоянные порядке лося, which doesn't really work grammatically, since порядке is locative and needs a preposition. But it's really very funny, since порядок means "order" ... but only in the sense of "arrangement" or "method" or "law and" sense of the word. As I said, this isn't really a good Russian phrase, but as much as it means anything it means "a permanent lineup of moose".