Addressing your concerns 

888fortune, I found your comments at Duke53's talk page that flesh out some of your concerns.  I'm glad to see them, and I'm sorry I didn't spot them before I left my earlier message.  I'd like to try to address some of those concerns.

If I'm not mistaken (and please correct me if I am), this seems to be your core concern: "I believe it is confusing to a person searching for that name to find another name."  You might be unaware of this, but Wikipedia has a "redirect" feature that can take a commonly used search term and re-point it to the article it refers to, if that article exists under a different name.  You can try this: type "The Wild Center" into Wikipedia's search box; it should take you to the Natural History Museum of the Adirondacks article.

From a reader's perspective, the redirect does have the potential to be confusing: "I typed in one thing, and the big headline at the article says something completely different!"  Naturally we don't want such confusion.  There are two things that can help.  One is that Wikipedia will show a little message saying "(Redirected from The Wild Center)" so the user at least knows they didn't somehow hit the "Random article" link or something like that.  Another one that the editors of the target article can do is to make sure the common search terms are mentioned.  In this case, the article's lead sentence highlights this by introducing "The Wild Center" as an alternative name, and it's in boldface so it's harder to miss.  A person searching on "The Wild Center" and arriving at the Natural History Museum of the Adirondacks article will probably not be very confused, since they'll see "The Wild Center" prominently displayed on the page, and since they'll more than likely already know that The Wild Center is a museum of natural history located in the Adirondacks, so the full official name is unlikely to surprise them.

You also say "I think that the Museum has the right to choose its own name."  I don't think anyone would disagree with that, but it's reasonable to think that the nickname "The Wild Center" could be in vogue for a few years and then replaced by another nickname. ("The Otter Stop", perhaps? )  If there's a stable, official name that will stick with it for as long as it's a museum, it makes some sense to use that name for the article title and to set up redirects for all of the popular nicknames.  The purpose of Wikipedia is not to aid the museum in marketing itself, but it's definitely reasonable to adopt some of the marketing phrases if that's how a significant number of people might identify the place.

Does this satisfy any of your concerns?  I'm interested in your response.  /talk/