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I’m afraid backward compatibility binds us here. For new code however, it would be nice to use one name consistently. My preference goes to "file", because I really like the print function, but I suspect this could turn into bikeshedding quickly :) I think this is too little an issue to warrant a line in the style guide. Maybe just watch python-checkins and comment when someone adds a function using "stream", "fp" or "fileobj". I suggest closing this report as wontfix.
You may want to open a new report about the matter of pprint and print having incompatible signatures. How about proposing a new function, say pprint.print, which could be a drop-in replacement for builtins.print?