Could this be some recognizable sentinel (<stream> or something better) rather than empty string?

This seemed the easiest way of doing it without complicating the logic and the tests. Also, I couldn't find a uniform way of dealing with a lack of "name" for BytesIO() objects in other libraries, so I did not want to introduce anything "new and specific".
Do you have an example (or an idea) of a sentinel use that would fit here? In that case, we could do a similar change for gzip, bz2, lzma, ... libraries to have a bit more standardized way of dealing with this situation when we have BytesIO() objects.