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.