You describe a pattern that never existed or which was abandoned very early on; Jeff Atwood's only criteria in the beginning were that 1) he "like" the name, and 2) the name be available. The proposed sysadmin-oriented site was initially called "IT Stack Overflow," before Server Fault was adopted in March 2009. The third site was named Super User because he was able to obtain the domain name. The fourth site was Meta Stack Overflow, which isn't even a play on technical terminology.
The cleverness of a Stack name is to some extent correlated with age, as in the early days of the company there was more interest in developing community, and greater resources put into not only the community names but in having distinctive visual styles as well. Soon, however, there was pushback that the network was becoming fragmented, and that it was too inefficient to spend so much time on names and designs. Nothing To Install was reverted to Web Apps, and while a few communities retained their brands (e.g. Seasoned Advice, Cross Validated), the decision was made to favor succinctness and commonality.
By 2013, the policy was that all sites would be [Subject] Stack Exchange, and I believe a few names were actually reverted to that format ("Travel Answers" comes to mind).