kestrell and I just watched this, and quite enjoyed it.
Regarding the names Adam & Eve, IMDB Trivia says:
Contrary to most viewers' assumption, Jarmusch did not name the two main characters directly after the Adam and Even of the bible; rather, he was referring to Mark Twain's satirical work The Diaries of Adam and Eve. Jarmusch told a Hollywood Reporter interviewer that "it wasn't until shooting the film that I realized everyone's first impression will be the biblical reference. Whoops. It's too late now. What can I do?" Twain's is one of the faces visible on Adam's wall of framed portraits in the movie.
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Regarding the names Adam & Eve, IMDB Trivia says: