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It'd be nice to eventually standardize on the kwarg name used for basic 
file-like args in the stdlib. print, warnings.showwarning and some 
others take a file= argument whereas pprint, getpass.getpass take 
stream=
print and pprint in particular should match -- though they do have a 
different option set, when you're using the same options this 
consistency would ease replacing:
print(obj, file=sys.stderr)
with
pprint(obj, stream=sys.stderr)

@Philip can you provide a patch so we can take this forward?

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?

Yes, simply saying "make it consistent" is a won't fix, because of backward compatibility issues. Specific proposals for specific functions in a way that deals with the backward compatibility issues should be opened as new issues.