Removing DRM does not typically change the contents of a file, except for the parts that specify the encryption keys, so any other identifying information will still be there.
Some Secure eReader ebooks used to include the owner's name in the text of the ebook, but this kind of "social" DRM has never caught on with the major DRM providers. I don't think Amazon or Adobe or B&N can tell who originally purchased and downloaded the ebook once DRM has been removed, but I am not 100% sure of this. I would be more nearly sure if I had converted the ebook in Calibre, e.g. MOBI to ePub (and back to MOBI if necessary) or even ePub to ePub.
I don't worry about this when removing DRM for personal use, but I if I was storing the ebooks in a cloud owned by an ebook vendor I might be more concerned (although not by much).
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