• Academy of the Four Elements: A classic and straightforward name that clearly communicates the school's focus.

• Elemental Academy: Simple, memorable, and emphasizes the core curriculum.

• The Hearthstone School: Evokes a sense of warmth and home, subtly referencing fire.

• The Verdant Academy: "Verdant" means green, suggesting a connection to nature and earth.

• The Aquamarina Institute: Sophisticated and hints at the water element.

• The Aethelred School of the Elements: A more unique name incorporating an old English name (Aethelred meaning "noble counsel"), adding a touch of history and prestige.

• The Four Winds Academy: A metaphorical reference to the elements, suggesting breadth and diversity.

• House of the Ember, Wave, Stone, and Zephyr: This option uses evocative words for each element and clearly indicates the house system.

• The Elemental Concordance: Suggests harmony and balance between the elements.

• The Crucible Academy: A powerful name suggesting transformation and forging character, referencing fire's transformative power.

• The Terra Firma Academy: "Terra Firma" means solid ground, referencing earth's stability and grounding influence.

• The Tidewater Academy: Evokes the fluidity and power of water.

• The Skyreach Academy: Suggests aspiration and reaching for the heights, referencing air.

• The Elemental Guardians Academy: Implies protection and mentorship, linking to the elements' power.

• The Elemental Harmony School: Emphasizes the balance and cooperation between the elements.

These names offer a variety of styles and tones, from formal and traditional to more evocative and imaginative. Consider your target audience and the overall branding you wish to create when making your final selection.