Finally I didn't find any way to get to know the assigned file name, because even it is not in the FTP server's response. My FTP server (vsftpd 3.0.2 under Ubuntu) for storeUniqueFile command simply answers
226 Transfer complete.
and I don't have any more information. The file is created usually with .1, .2, etc. extension. If I was sure that nobody uses the ftp server concurrently, I could run a listFiles() before and after and simply make a diff. That is all :-(