#Only if the monk recognizes the casting of the spell
Only if the monk recognizes the casting of the spell
Charm Person states
When the spell ends, the creature knows it was charmed by you.
This means that during the duration of the spell, the target doesn't know that it's being charmed, and thus cannot use Stillness of Mind to end the charm.
The charmed effect would break down if the target is aware that it is charmed only from the status effect. This knowledge would allow the target to act in a manner contrary to being charmed ("I know that it's only the charmed effect that's making me not want to attack this creature, so I'll attack it anyway"), and thus eliminate the effects of being charmed in all cases. I'd argue that making the saving throw against being charmed would represent this realization.
However, in the case of Charm Person, it's possible that the monk could see and recognize the spell being cast (see this question), and know that he/she is being charmed. This knowledge, which is separate from the status effect itself, would allow a target to know that they are being charmed. The target would have to recognize the source of the magic (a wizard casting a spell, or a vampire using its magic powers) and the effects of the magic (this spell causes people to be charmed) in order to figure out that they themselves are being charmed.