I am wondering why some possessive nouns does not have apostrophes.
If "America's Credit Union" has an apostrophe, why not "World Health Organization"?
My intuition says that the apostrophe is only needed if the noun refers to a specific being. In the above example, "America" refers to a specific country, and "world" is somewhat vague, as does not exist such entity called "world".
Is this correct? What would be the formal explanation?
It is the formal name of the organisation. End of.
Organisations can and do choose names without regard for grammatical rules. Not that I am saying that this name is ungrammatical. My point is that rules do not apply to names.
I don't believe there is a rule about specificity or individuality in terms of possessive nouns. You can be a "horse's ass" or a "tavern's patrons" or a "year's worth of whiskey." A year is a pretty non-specific, immaterial idea to possess something, but nevertheless, that is the usage. It's a "world's fair" even though it's created and hosted by one country (with other countries' participation).
Many uses of possessive apostrophe are arguable, or simply traditional, and not always logical. In the examples given in the question, there is a difference in meaning or connotation.
The health organization is concerned with the world's health, or with health around the world, but it is not owned by or possessed by the world. And, it does count for something that "World Health..." is easier to say than "World's Health...."
Put another way, the "League of Nations" could also have been the "Nations League" and the "United Nations" (simple plural), or the "Nations' League" (possession of the nations).
"America's Credit Union" is trying to suggest that it "belongs to" America; although of course, it doesn't.
