How did devil may cry get its name

Devil May Cry got its name from a line that Lady said to comfort Dante during the end of DMC3. After losing Vergil in the Underworld, he came back to Lady, returning her rocket launcher, Kalina Ann, and stating that the demons were gone but will be back very soon. She looks up to him and sees what she never expected from a demon. Lady: Are you crying? Dante: It's only the rain. Lady: The rain already stopped. Dante: Devils never cry. Lady: I see. Maybe somewhere out there even a devil may cry when he loses a loved one. Don't you think? Dante: Maybe.