I would call Stack Overflow "Stack Overflow", just like I would refer to other specific sites by their names (Super User, Arqade, Programmers, etc.).
It really depends on what you're writing about, I think. You could say "Stack Overflow, which is a part of a larger Stack Exchange network of Q&A sites" or something along those lines.
Stack Exchange is also the name of the company, so if you're talking about that... call it that.
If you're writing about the network in general but want to inject a familiar name, something like "The Stack Exchange network that includes sites like Stack Overflow and Server Fault..." could work.
You get the idea.
There's also the section on proper use of our name in the Trademark Guidelines:
Stack Exchange Inc. is the official name of the company.
Stack Overflow is a programmer Q&A site on the Stack Exchange Network. As a name, Stack Overflow, is always written "Stack Overflow"
(two words, capital letters). The website domain name is always
written stackoverflow.com (no CamelCase, single word
capitalization rules apply). Currently, all Stack Exchange Network
sites follow this convention: Server Fault (serverfault.com), Super
User (superuser.com), etc.
A Stack Exchange site is a Q&A
website built on the technology of Stack Exchange Inc. The phrase
"Stack Exchange" is generally used as an adjective, not a noun. One
would say "Propose a Stack Exchange site on Area 51" (correct), not
"Propose a Stack Exchange on Area 51" (wrong).
The Stack Exchange
Network refers to the collection of Stack Exchange sites and
Area 51 (two words) is the site used to propose new Stack Exchange sites for the Stack Exchange Network.
The Stack Exchange API
allows users to write applications based on the Stack Exchange engine.
The API is always referred to as "Stack Exchange API", even if the
application is written for a specific site (i.e. never Stack Overflow
API, Server Fault API, etc.).
The Stack Exchange Blog is the
company blog which talks about everything we're doing on all our sites
and what the company itself is doing.
(If these guidelines change and this answer isn't updated, ignore what's here and go with the official version on the page linked above.)