…or is this site's name a combination of Stack Overflow and an exchange of ideas?
I can't say with absolute certainty, but I'm fairly sure this is the correct explanation. While one might speculate there was some influence by the proximity of the FogCreek offices to the New York Stock Exchange, "StackExchange"* was originally intended to be sold as a product – a customized version of Stack Overflow for your own topic(s).
Products have marketing, and the promotional blurb on the FogCreek site at the time refers to the offering as the "
StackExchange** Stack Overflow Knowledge Exchange platform", suggesting that the name is very likely a portmanteau of "Stack Overflow" and "Knowledge Exchange".
*The space was added sometime later, as it's consistently absent from the early material
**Joel points out in the comments this was actually a typo