I have bought a book online, then downloaded it on my computer, but I chose to continue without an ID (I didn't know anything about the digital editions yet). After I downloaded the book I knew that it can't be downloaded on another computer. Originally the book is not for me. Is there any way I can add this book to an ID?
That is not possible. You can only ask by the reseller of the eBook if you can download the eBook again with the other ID new. (You need a new eBook not only a new file).