Other names frequently used instead of or with For Elise
Naming Classical Pieces
As with most other composers in his time, Ludwig van Beethoven rarely named his own compositions. Most classical compositions got their name by what type of music it was followed by the key in which it was written, and lastly a number based on the composer's previous works of the same type. Another name you might find Für Elise under is 'Klavierstücke' (WoO 59) which literally translates into 'piano piece' from German.
As implied by the name, a bagatelle is usually short and somewhat whimsical in nature. Für Elise begins in light and smooth motions, but later branches into two other parts that are indeed unpredictable and a departure from the original and well known theme that recurs throughout. The piece is actually written in the rondo form; in a rondo, the first theme is played, then a second development is introduced and played before returning back to the first theme again, then into a third development, and then back to the first theme again. This is also referred to as A B A C A, where 'A' is the first theme. There can be more than two other developments in a rondo, but this is the most common.
A minor (the key signature)
Under normal circumstances you don't need to get very far into music theory before key signatures are covered. It's a normal practice to add the signature of a composition in its name, and although this has been deprecated in most modern music, it is still utilized by lots of composers around the world.
Often when a composer publishes music he assigns it an opus number. Beethoven only gave opus numbers to what he considered his most important works, such as the grand symphonies, his piano sonatas, and other larger scale compositions. This meant a lot of his smaller compositions were left without an opus number, and they were later given a WoO, or werk ohne opuszahl, which is German and translates to work without opus number. In this particular case the WoO number was decided in 1955 by Georg Kinsky, long after the composer's death in 1827.
Opus: Latin for work, as in a work of art.