The name means seeded apple. It came from Old French pome grenate, from the Latin pōmum, fruit or apple, and grānātum, full of seeds. Medieval English spelled it dozens of ways, from pomegarnet to poungarnet, before pomegranate won.
The -ate at the end is unstressed, so it shrinks to it, as in granite, climate and private. This follows a general English pattern: -ate in a noun or adjective is usually weak, while -ate in a verb is ayt. Compare the adjective separate, SEP-uh-rit, with the verb, SEP-uh-rayt.
The main stress goes on the first syllable, with a lighter stress on gran. The first vowel differs: PAH in American English, POM in British English.