Naturally, demons do not reveal their existential names, their mark upon the world... However, for what Raphaeline gambled, she had to do it. She gave her name to Vergil.
Revealing an existential name is an act of extreme vulnerability for a demon. That name, more than just an identification, is the essence of their existence.
For demons, offering such a name is not merely opening the door for someone to understand them; it is handing over the key for their very essence to be shaped or destroyed.
"If you win, my soul is yours."
To offer one's soul is exactly to offer one's essence... Vergil would naturally be confused; he knows little about this. About the true power of demons when absorbing souls...
Raphaeline knew this. She knew very well what she was risking when she accepted Vergil's gamble. But, back then, arrogance had spoken louder.