The question is not why K. 550 has no nickname, but why a few other of
WAM's symphonies have them.  It was not common practice to nickname works
- names like "Prague", "Linz", "Jupiter", "Haffner" were not given to those
symphonies by Mozart.  And out of about 50+ symphonies he wrote, only a few
were nicknamed at all.  Nicknames like that are usually given by posterity
- why nobody gave a nickname to this symphony? What about K. 543, doesn't
this one "deserve" a nickname? Perhaps nobody thought of nicknaming K. 550
because it's one of only two symphonies in a major key, so there was no
perceived need to distinguish it further? (People sometimes refer to K.
550 as "great g minor" and K. 183, "little g minor".) I'm afraid no
scholar can tell you why nobody thought of a name for this or that work
of Mozart.

Whether this work was written during a "very sad period", we don't really
know.  We know extremely little about the year 1788 in Mozart's life,
although we know that he asked his friend for money.  As somebody on the
net put it very aptly, Mozart had "cash flow problems".  We know that with
the Austro-Turkish war, the demand for music was diminished and the number
of concerts in Vienna went down.  As for the information about Mozart's
life, most of it comes from the correspondence between Wolfgang and
Leopold.  Once Leopold died (in 1787), the correspondence stopped.  It's a
pity that Mozart and his sister didn't write to each other in those years:
we would have a great source of information.

-Margaret