Originally Posted by supermasterphil

No, not even every Lufthansa plane has a name but most of them have. As I usually have my logbook with me, I always ask the captain to fill it out anyway, including tail-number. So it's pretty easy to get the name.
Check out this website.

Unfortunately, I don't know where you can look up which plane served which flight but Oliver2002 had a website the other day that was pretty good. I don't remember it though.