I need to find this font so I can purchase it. What is it's real name?
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Look here <http://store1.adobe.com/cfusion/store/html/index.cfm?store=OLS-US&even t=displayFontPackage&code=1766> for Adobe's offerings in terms of Helvetica Neue. And yes, the font family name is in fact Helvetica Neue. Each member of the font family (51 styles in total) has a name that begins with Helvetica Neue Std.
FYI, Helvetica Neue is not a WIndows system font. It is a system font that is bundled with recent versions of the MacOS with some form of the words Helvetica and Neue in the name of the font. If you opened an InDesign document with that font missing, it is likely (but not necessarily) a document recently processed on a Macintosh.
Unless you get the font file itself from whoever created or last worked on the document and used that font (assuming that the font is either an OpenType or a Windows format TrueType font and that you can legally use the font), you may need to separately license Helvetica Neue from any one of the font foundries with a Helvetica Neue family. The name might not match exactly (actually, probably won't match exactly) and you may need to make adjustments in your document to use name of the font that you do license.
FWIW, your experience is not uncommon. There are hundreds of different variants of Helvetica, Times, Arial, etc. that share the same names, but are slightly different. In this particular case, having a slightly different name is probably for the best if you can't get the exact same font, because it will force you to look for any problems that the replacement font may cause (slightly different metrics, styles, etc.).
As far as I know, Apple does not license its version of HelveticaNeue for use on other platforms and even if the font is in OpenType or Windows TrueType format and could be copied to a Windows system, you are probably in violation of the licensing conditions for that font under MacOS X. The closest you may come to the exact HelveticatNeue on the Macintosh may be available from Monotype or Linotype on-line at their web sites.