Custom-branded site names (like "Cross Validated", "Ask Different", "Seasoned Advice") were from a time when communities would discuss what their up-and-coming site would be called and (theoretically) the best option would be selected. Unfortunately, crowd-sourced naming discussions often became highly toxic and divisive to the community, so after a lot of discussion and debate, we ultimately decided to forego the naming exercise entirely.
Sites are now labeled by the subject space they cover. When a proposal approaches the end of Definition, it undergoes a final evaluation by the Community Team. During that process, it is discussed if the proposal title best matches the questions actually posted — many of those discussions have already been raised by the proposal community — so if there is a decisively better name, the proposal may be edited. If there's still a question or debate about what the site should be called, a discussion is raised with the community.
The URL for a site typically defaults to the site title as close as reasonable; redundant words are often removed (French Language → french). But if there is a well-established and easily recognizable way to abbreviate a subject name, the shorter version may be used (computer science → cs; Science Fiction & Fantasy → scifi;).
This process has changed over time, so you may be able to find exceptions, but the vast majority of sites have been named as described here.