Ben G. answered 10/17/20
BM in Piano Performance, currently pursuing a MM in Piano Performance
This is a great question! You are correct in thinking it is not called a nocturne because it is included in a larger work. The nocturne is a genre which was invented by Irish Composer, John Field and then strongly championed later on by pianist and composer, Frédéric Chopin. Although "Claire de Lune" from Suite Bergamasque subjectively evokes the intimate nocturne "sound world", piano nocturnes exist as stand alone pieces completely unrelated to larger works; such as the suite or sonata.