The female character in "Hills" actually does have a name -- "Jig" -- but it is used very sparingly by the male, and it may be a nickname rather than a proper name. Hemingway chooses, however, to refer to her as "the girl" throughout the piece, which certainly supports the idea of a universal problem (and also stands in stark comparison to the fact that the male character is referred to as "the man" -- why is she only "a girl?")
It will probably be important to note that her lover calls her by name, but that Hemingway chooses not to.
By not naming his characters in "Hills Like White Elephants," Hemingway makes their situation, and the thing they are unable to talk about, universal to everyone. However, I think you've done a pretty good job of presenting your argument in your comments above. Rather than focusing on the names, or lack thereof, you might use as your thesis the fact that each story contains an unspoken conversation that the ready is allowed to "hear" only through the thoughts and actions of the characters.
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