Because sounds Cool. Just like why they decide to call Lucifer's Call in EU.
SMT3 was the first Mainline SMT that had a localization , so they couldn't exctally call just Shin Megami Tensei III , when they and still didn't released 1 and 2 here, people would be confused.. Also Shin Megami Tensei isn't exctally the english name out there, they had to put something more common, hence Nocturne.
It seems the original Japanese version was also called Nocturne. In fact out of Japan we received a version called SMT III Nocturne Maniax, but the Maniax subtitle was localized out of the cover, which was a special edition that added Dante and the True Demon route.
According to the wiki, at one point in development it was going to be called SMT: Vortex, refering to the Vortex World. My speculations are that Nocturne may had been used either because of how it contrast with its predecesors, breaking the formula of the classic Law vs Chaos narrative, or perhaps is because the Kagatsuchi plays an important role both in the gameplay and the story and it kinds of looks like a moon shinning on the vortex world.
And because it sounds cool.