Neapolitan

From Latin neāpolītānus, from Neāpolis, from Ancient Greek Νεάπολις (Neápolis, literally “new city”), a Greek city in modern Naples. Doublet of naporitan and Napolitano.

The ice cream combination may be so called because one version popular in the late 19th to early 20th century was green (pistachio), white (vanilla) and red (cherry or strawberry), the colors of the Italian flag, or due to some ice cream makers being from Naples; Italy's reputation for ice-cream making may have reinforced the perceived connection.