Here are some MHA-style name options for your character, considering her traits and backstory:

Hero Names (reflecting power and duality):

• Umbra Witch: Combines the Latin word for shadow ("umbra") with a classic villainous archetype, highlighting her dark magic while hinting at a potential for control.
• Nightshade Sorceress: Evokes a sense of mystery and danger, reflecting her dark magic and unpredictable nature. "Sorceress" adds a touch of elegance, contrasting with her psychotic tendencies.
• Obsidian Heart: "Obsidian" represents the dark, powerful nature of her quirk, while "Heart" suggests a hidden vulnerability or a core of rationality.
• Shadow Weaver: This name emphasizes her control over darkness and implies a manipulative, strategic approach to combat.
• Lunar Eclipse: A more poetic name, suggesting the cyclical nature of her personality (rationality and psychosis) and the powerful, transformative nature of her quirk.

Villain Names (emphasizing the psychotic side):

• Nightshade: Simple, yet effective in conveying a dark and dangerous persona.
• Voidbringer: Suggests a character who brings chaos and destruction.
• Raven's Shadow: A more ominous name, hinting at ill omens and a dark, brooding personality.
• The Ink Witch: This name is more evocative and mysterious, suggesting a character who manipulates shadows and darkness with ease.
• Kurohime (Black Princess): A Japanese-inspired name that hints at a powerful, yet potentially cruel, ruler of darkness.

Names that blend hero and villain aspects:

• Kuroi Tsuki (Black Moon): A Japanese name that blends darkness ("Kuroi") with the celestial imagery of the moon, suggesting a duality of light and shadow.
• Aethelred: An Old English name meaning "noble counsel," which ironically contrasts with her rebellious and often irrational behavior. This creates a compelling internal conflict.
• Nyx's Daughter: Nyx is the Greek goddess of night, linking her directly to darkness and power. "Daughter" suggests a lineage or inheritance of dark magic.

Considerations for choosing:

The best name will depend on the specific tone and direction you want to take your character. Consider which name best reflects her internal conflict, her power level, and the overall story you're telling. You can also combine elements from different names to create something unique. For example, you could combine "Umbra" with "Witch" to create "Umbra Witch," or "Nightshade" with "Sorceress" to create "Nightshade Sorceress."