OP’s claim is that cults give nicknames.

Post-Hoc Ergo Proper Hoc Fallacy. "Cults give nicknames, therefore if you give someone a nickname you're a cult" doesn't logically follow.

you likely have an inherent bias

Casual Fallacy. The existence of individual bias does nothing to affirm or reject a claim

If we were weighting on bias, your extreme reaction to a casual anecdote would disqualify your observations immediately.