I hardly ever get worked up about what you call some things (whereas I really care about others). It's not my job to name things, or at least the things that aren't important, like what you'd call a product or service that you are selling.
The discussion I found really amusing today was on the "Is HIE a noun or a verb?" It really depends on what you are selling I would guess. If you "are" an HIE, then you are selling yourself, and the services provided by your organization, so you'd probably fall on the noun side of this debate. If, on the other hand, your customers are "HIE" (noun form), or others who need exchange services, then you'd probably fall on the "verb" side of the debate.
Linguistically, the phrase "Health Information Exchange" parses ambiguously as either a noun or a verb. The first two words "Health Information" are descriptive of either the kind (of noun), or the subject (of the verb). And exchange itself is ambiguous. As a verb it is the trade of information. As the noun, it is the act or place where such trades occur.
Does it matter what "we" agree on? No. The word will still be ambiguous because usage creates definitions, not the other way around.
One of my followers pointed out that Name = Brands = Function = Market, and referenced Kleenex, Ziplock, Web, Chapstick, Coke and Sharpie. I'll point out in response that it was the product that came first, then the name recognition that established the brand and subsequently the market. While the name was important, what made the name successful was the product it was applied to, NOT the other way around.
Arguably, a bad name can kill a good product or service. But I've never seen a good name save a bad product or service. In fact, a bad product or service can kill a good name. Did you see what happened to United stock when they broke his guitar?
Don't worry about the name. Worry first about the product or service. Even a silly name can become a great brand, but it never would have happened if the product hadn't tasted so good.