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Why is it called WoO 40 or Hess 238?

These are names of Beethoven's symphonies.

They have peculiar names.

Compositions are commonly referred to by what we call opus numbers. A famous sonata by Beethoven is his Opus 53, and—because "opus" is Latin for "work"—this is an identifier that tells us that it is his 53rd work (more or less).

But there are a couple problems with this system:

1. Sometimes, composers don't give a composition an opus number. For this reason, Beethoven scholars sometimes use WoO numbers. "WoO" is short for "Werke ohne Opuszahl," which itself is German for "works without opus number." As such, the WoO system helps categorize and identify works for which we don't have an opus number.


2. In other instances, opus numbers don't show a clear chronology. Typically, opus numbers are given in ascending order when they are written; a composer's first work is Op. 1, their next work is Op. 2, etc. But sometimes opus numbers are given in a different order, and so Op. 9 wasn't always written before Op. 10. Moreover, sometimes sketch fragments or unfinished pieces that did not receive opus numbers are important relics for following a composer's development (and therefore need to be catalogued). In cases like this, we devise other systems to categorize a composer's output. In Beethoven's case, Willy Hess published a catalogue in 1957 of Beethoven's work that includes sketches and unfinished works; Hess 238 is thus a listing within this Hess catalogue. (Perhaps surprisingly, Hess's catalogue isn't the only one for Beethoven's works!)

It's worth mentioning that other composers have similar systems: see the Köchel catalogue for Mozart's works, the Deutsch catalogue for Schubert, or the Hoboken catalogue for Haydn (coincidentally also written in 1957). Sometimes these works are listed by genre—all piano sonatas are numbered together, all string quartets are numbered together, etc.—but other times they are listed chronologically.

You got that wrong, WoO is no name, but a sort of disambiguation between the different works of a composer. While opus is used by many composers (they assigned the numbers themselves), they are not very reliable and often incomplete. Professional listings have different names, frequently taken over from the creator of that listing. Sometimes even more than one such listing exists for the same composer (Scarlatti sonatas e. g. by Longo, Kirkpatrick, since additional research suggested a revision.)

There are other kinds of disambiguation, like adding the key, see this question and its answers, and for symphonies often just the ordinal number is used. Especially for Beethoven the ordinal number (or a catching title like Pastorale) will much more likely be recognized than any listing reference.