Here are some MHA-style names fitting the description, playing with variations on "Hawk" and incorporating the white wing theme:

Elegant & Graceful:

• Alba Ala: "Alba" meaning white in Latin, combined with "Ala" (wing in Spanish). Suggests a graceful, elegant hero.
• Lumina Volans: Latin for "Shining Flyer," evoking a sense of ethereal beauty and speed.
• Cynthia Pluma: "Cynthia" is a name associated with the moon, adding a mystical element, paired with "Pluma" (feather/wing in Spanish).
• Blanca Avia: "Blanca" (white) and "Avia" (bird) in Spanish, simple yet evocative.
• Seraphina Alata: "Seraphina" suggests angelic qualities, combined with "Alata" (winged in Latin).

Strong & Powerful:

• Glacies Falx: "Glacies" (ice) and "Falx" (sickle), suggesting sharp, powerful wings capable of icy attacks.
• Apex Nimbus: "Apex" (highest point) and "Nimbus" (cloud), implying a powerful, cloud-like flight.
• Stormwing: A straightforward but powerful name suggesting a fierce, white-winged hero.
• White Wraith: Evokes a ghostly, swift, and powerful image.
• Avalanche Astra: "Avalanche" suggests power and "Astra" (star) adds a celestial touch.

Mysterious & Intriguing:

• Lunar Zephyr: "Lunar" (moon) and "Zephyr" (gentle breeze), creating a mysterious, swift character.
• Silken Shadow: Suggests a stealthy, graceful hero with white wings.
• Ghostwing: Simple, yet evocative of a mysterious, swift character.
• Crystalline Gale: "Crystalline" suggests the delicate yet strong nature of the wings, and "Gale" implies speed and power.

Unique & Creative:

• Cirrus: A type of cloud, suggesting a light and airy yet powerful flight.
• Plume: Simple, elegant, and directly related to feathers and wings.
• Albatross: A large seabird known for its powerful wings.
• Snowdrift: Evokes the image of a powerful, white-winged hero.

Remember to consider the overall personality and fighting style you envision for the character when making your final choice. These names offer a range of options to inspire your creative process.