You don't have to be fearful about Labels because if anyone wants to steal your bitcoin, moves it out of your wallets, they must have access to your Bitcoin private keys. If they don't have access to private keys, your bitcoin is safe.

With either labels or public keys, nobody can move your bitcoin.

You actually need to avoid to label or post your public keys, public addresses on Internet, to inform like "I am a Bitcoin millionaire/ billionaire". It's dangerous and need to be avoided because you are labeling you as a rich investor, and you will become favorite targets of either Hackers or Physical attackers.

Bitcoin Physical Attacks.