So far, the known Namesakes and their “worlds” are: Alice (Alice in Wonderland), Jack (Jack and the Beanstalk), Wendy (Peter Pan), and Dorothy (The Wizard of Oz). What do all these characters do in their respective stories? They're people from the “normal” world who go to far-away lands and change things while they're there. Hence the premise of the comic.
The secret society devoted to protecting Namesakes is named Calliope. In Classical Mythology, Calliope is the muse of epic poetry.
When telling the story of the Dorothies they say that they "never age but always die" and in the monument to the Dorothies, we see a long row of human skeletons laid out on the floor. This could be taken to mean that almost all of the Dorothies since the original have died in Oz... which is to say that they never went home.
Not really. If the canon of the first six books is the same as each Dorothy's adventure, then they actually all went home; then came back later to live in Oz forever (Possibly with relatives).