Multipart mp = (Multipart) message.getContent();
        for (int j = 0; j < mp.getCount(); j++) {
            Part part = mp.getBodyPart(j);

            String disposition = part.getDisposition();
            if ((disposition != null) && ((disposition.equals(Part.ATTACHMENT)) || (disposition.equals(Part.INLINE)))) {
                BufferedInputStream in = new BufferedInputStream(part.getInputStream());
                BufferedOutputStream out = null;
                byte[] buf = new byte[65535]; 
                fileName = MimeUtility.decodeText(part.getFileName());  //!!!!!!!!!! Тут пусто
               
       }

part.getFileName()

for (int j = 0; j < mp.getCount(); j++) {
            mp.getBodyPart(j).getFileName();
...
}