Sorry for any repeats!
Fire:
Blaze / Blaise
Ember
Auburn
Scarlett
Brantley (means "fiery torch")
Brinley (means "burnt meadow")
Ash / Asher / Ashton / Ashley / Ashlyn
Enya (means "fire")
Flint
Hayden (means "fire")
Ignacio / Ignatius (both mean "fire")
Phoenix
Seraphina / Serafina (means "ardent/fiery")
Apollo (he drove a fiery chariot through the sky, according to Greek mythology)
Earth:
Adam (means "son of the red earth")
Demeter (means "earth mother," Greek goddess of fertility)
Hermione (means "earthly")
Tara / Terra (means "earth")
Amber
Sienna
Sierra
Autumn
Briar
Clover
Dawn
Eden
Fern
Camden (means "winding valley")
Forrest
Flora
Hazel
Stone
Canyon
Heath
Everest
Jade
Meadow
Olive
Rosemary
Sage
Savannah
Gaia (means "earth mother")
Tree Names: Aspen, Magnolia, Acacia, Ash, Cedar, Juniper, Pine, Linden
Flower names: Azalea, Lily, Violet, Daisy, Rose, Lavender, Calla, Blossom, Dahlia, Holly, Ivy, Iris, Jasmine
Water:
Kai (means "sea")
Brooke
Marina
Nile
Marsh
Hudson
River
Bay
Caspian
Jordan
Wade
Cordelia (means "daughter of the sea")
Rain
Beck (means "stream")
Calder (means "stream")
Douglas (means "dark river")
Dylan (means "son of the sea")
Hurley (means "sea tide")
Lachlan (means "from the land of lakes")
Maxwell (means "great stream")
Murphy (means "sea warrior")
Ford
Ginevra (means "white wave")
Isla
Jennifer (means "white wave")
Maris (means "of the sea")
Lynn (means "lake")
Nerissa (sea nymph)
Rio
Talullah (means "leaping water")
Air:
Skye
Storm
Aura
Zephyr
Niall (means "little cloud")
Brisa (means "wind")
Stella (means "star")
Iris (means "rainbow")
Jonah (means "dove")
Celeste
Neil (means "cloud")
Aria (means "air" in Italian)
Gale (strong wind)
Bronte (means "thunder")
Guthrie (means "free wind")
Sora (means "sky")