Cor! That's old documentation!
.. the information included in a font file ..
There is No Such Thing as "a" font file. What sort of files are you referring to? DFONT? Type 1? Truetype? Opentype? Your mentioning a "name" table suggests the latter.
Let's get the most important bits right first. I'm surprised you refer to that old page, because it's last updated around 2003 (and frankly even that late date surprises me). The reason for that is because that particular sub-site of Apple's deals with (their version of) Truetype, and Truetype fonts have long been abandoned by everyone in favour of the Opentype format. True, it's more or less the same, but you should be reading stuff like
http://www.microsoft.com/typography/otspec/
or
http://www.adobe.com/devnet/opentype.html
(the latter refers back to the Microsoft site for the main documents but still contains lots of useful additional info).
Regarding the format of the 'post' table: this is, actually, still relevant for Opentype fonts. There are different formats in which the data can be stored; you should read the format first and then decide what else you need to know. But before I get your hopes up: one of the formats that is used frequently is type 3: 'explicit no-name table', which means there are no glyph names stored in the file (they might be stored as part of the CFF data in a Type 1 style OTF, which is yet something else).
But yet again, this might be not what you were after. The 'post' table allows access to unique glyph names in a font, for example, a regular 'A' that is called 'A' and an alternate A called "A.alt". Perhaps what you describe would best be achieved by examining the character map instead -- 'cmap'. (Read the documentation I referred to why I believe this.)