Great Idea.

Perhaps call it something like:

BeeOff: A play on “bee” similar to Honey, but with a focus on avoiding (off) certain products.

BoycottBee: Directly stating its purpose as a boycott tool.

Avoidify: Emphasizes the idea of avoiding certain products or brands.

BlanketBan: Suggests a comprehensive avoidance or ban.

NectarNone: Opposite of honey nectar, focusing on avoiding products.

ProtestPal: A friendly companion for those who want to make a statement by boycotting certain products.

SentryShop: Acts as a guardian or sentry while shopping, warning against certain products.

Ethico: Emphasizes ethical consumption by avoiding certain brands or products.

NoGo: Simple and direct, signaling products to avoid.

BlockBuy: Directly blocks purchases of unwanted products.

SanctionShop: Implies a personal sanction or restriction on certain products.

ProtestPulse: A tool that keeps the pulse of your protest or boycott efforts.

Avoida: A playful name emphasizing avoidance.