See the full usage document linked from the legal link in the footer:
Guidelines for the Use of the Stack Exchange Trademarks
The excerpt (below) is a little more rigidly formal than using (unofficial) terms like "the Trilogy" but this is how the name use is described under...
Stack Overflow Internet Services Inc. is the official name of the company, but you are welcome to say Stack Overflow Inc. to disambiguate between the site for programmers and 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 Overflow 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 services.
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 Overflow Blog is the company blog which talks about everything we're doing on all our sites and what the company itself is doing.