In Europe, EA has trademarked “Plants vs. Zombies: Battle for Neighborville”. Electronic Arts confirmed last month that the next Plants vs. Zombies shooter was entering a Closed Alpha. The game was referred to as “Codename Picnic” in the email for Alpha testers.
So, it seems that “Codename Picnic” or Garden Warfare 3 is officially called Plants vs. Zombies: Battle for Neighborville. You can take a look at the official filing here.
We should expect an announcement or trailer sometime relatively soon, as it seems everything is finally coming together.