A composer, or more specifically a 'symphonist', although the latter word is not used very often.
A composer.
... is called the composer.
A Librettist
The end of a symphony is called a rondo or sonata.
Whatever the person that wrote it wants to call it. Symphonies can have all sorts of variations in number of movements. Stravinsky wrote a piece he called "Symphony in Three Movements". Mozart's "Prague" Symphony (No. 38) has only three movements and is sometimes called the symphony without a minuet. Schubert's "Unfinished" Symphony only has two movements, thought presumably it was not planned that way. In the final consideration, it's best simply to go with whatever the composer called it.
A person who studies or writes history is called a historian.
A person who writes with their left hand is called left-handed or sinistral.
A person who writes laws is called a legislator or a lawmaker.
Testator.
The person who writes a check is called the payor. Or in the case of my brother, a sucker, when he writes another check for his girlfriend.
An author.
a publisist a bigraphy
composer
a playwright
This is a poet
A person who writes newspaper articles is called a journalist or a reporter.
hitorians