Air:
Alya- 'sky'
Alia
Aria- 'air'
Amaterasu- 'shining over the heavens'
Anan- 'cloud'
Anani
Anemone- 'wind'
Anil- 'wind'
Araceli- 'altar of the sky'
Acacelia
Aura
Anvidr- 'wind'
Abelia- 'the breath'
Alizeh- 'wind'

Birdie
Blue
Bayu- 'wind'

Cerulle
Caelestis- 'of the sky'
Cerulis
Celeste
Cosima

Era- 'wind'
Esen- 'wind'
Eteri- 'air'

Flurry

Gale
Guthrie- 'places full of free wind'

Heirani- 'heavenly crown'
Hodei- 'cloud'
Houa- 'clouds'
Hawk
Haneul- 'sky'

Ilma- 'air'
Ilmatar- goddess of the heavens
Inanna- 'lady of the heavens'
Iris

Jonah

Lani- 'sky' or 'heaven'
Lark
Luna

Misty

Nephele- 'cloud'
Nova
Neil
Niall
Naseem- 'gentle breeze of soft air'
Nimbus

Pilvi- 'cloud'
Paloma

Rangi- 'sky.' God of the sky

Samira- 'air'
Samir
Sora- 'sky'
Skye
Sky
Stella
Storm
Stormy
Saar- 'strong wind'
Scirocco- 'hot air and dusty wind'

Tumulus
Tsisia- 'of the sky'
Tsiuri
Tsisana
Tuuli- 'little wind'

Vayu- god of air and wind

Wren

Yun- 'cloud'

Zeru- 'sky'
Zeus- 'sky'
Zephyr- god of the west wind

Fire:
Agni- 'fire'
Alba- 'dawn'
Anatolius- 'sunrise'
Anatole
Aodh- 'fire'
Apollo- god of the sun
Aurora- 'dawn'
Aušra- 'dawn'
Avtandil- 'sunshine heart'
Azar- 'fire'
Aidan- 'fiery'
Amarkeeri- 'eternal flame'
Ash
Adara- 'fire'
Angarika- 'flames produced in the forest'

Belenus- 'bright'
Brighid- Irish goddess of fire
Bridget
Bryni- 'flame'
Blaze
Blaise

Cináed- 'Born of fire'
Cassia
Cyrus- 'sun'

Dian- 'candle'
Drita- 'light'

Eguzki- 'sun'
Eos- goddess of the dawn
Enya
Elio
Ember

Fajra- 'fiery'
Fiammetta- 'flame'
Fioralba- 'flower of the dawn'
Flint

Haul- 'sun'
Helene- 'torch'
Helios- god of the sun
Hestia- goddess of the hearth

Infernus
Ignatius- 'fiery'
Inti- god of the sun
Iskra- 'spark'

Joash- 'God's father'

Keahi- 'the fire'
Kenneth- 'handsome man born of fire'

Lavis
Lucasta- 'pure light'
Lucia- 'light'
Lucinda
Lugus- 'light'
Luminita- 'light'
Luz- 'light'
Leo
Langa
Lesedi- 'light'
Lebone

Magmis
Mzia- 'sun'
Mishal- 'bright flame by a source of light'
Mogotsi- 'someone who lights the earth'
Maletshatsi- 'the daylight's sunshine'
Mmakganya
Masana- 'the sunshine'

Narangerel- 'sunlight'
Nina- 'fire'
Noor- 'light'
Nkanyezi- 'star'
Naledi- 'star'
Nomalanga- 'sunny'

Or- 'light'
Ori- 'light for me'
Orion

Pele- goddess of volcanoes and fire
Photine- 'light'
Plamen- 'fire'
Pyyrhus- 'fire red'
Phoenix

Ravi- 'sun'
Roxane- 'dawn'

Smulder
Säde- 'ray of light'
Sahar- 'dawn'
Samson- 'sun'
Saulė- goddess of the sun
Savitri- 'relating to the sun'
Seraphina- 'fiery one'
Shachar- 'dawn'
Shula- 'flame'
Sirius- 'burning'
Sol- 'sun'
Soleil- 'sun'
Solveig- 'strength of the sun'
Sorin- 'sun'
Sunçana- 'sunny'
Sunna- 'sun'
Sunniva- 'gift of the sun'
Surya- 'sun'
Scarlet
Scarlett
Sunny
Summer

Tesni- 'warmth of the sun'
Tinatin- 'light'
Tanwen- 'white fire'

Vulcan- god of fire
Vesta
Volcanis

Zerah- 'dawning'
Zora- 'dawn'
Zorya

Water:
Aquifis
Aalto- 'wave'
Afon- 'river'
Agam- 'lake'
Alda- 'wave'
Arethusa- 'nimble water'
Asherah- 'she who walks in the sea'
Ariel
Azura
Assana- 'waterfall'

Belinay- 'reflection of the moon on a lake'
Burim- 'spring'
Brooke
Bay
Brooks
Bourne

Chillis
Calypso
Caspian
Coral

Damla- 'water drop'
Darya- 'ocean'
Delphine
Delta
Dylan

Euria- 'rain'

Fross
Finn
Flynt- 'stream of water'

Gal- 'wave'
Ghadir- 'pond of water'

Hai- 'sea'
Heremoana- 'dear ocean'
Hudson
Hurley
Halcyon

Icilis
Iara- 'water lady'
Ibai- 'river'
Indra- 'possessing drops of rain'
Isla

Jubal- 'stream'

Kai- 'sea'

Laine- 'wave'
Llyr- 'sea'
Lwandle- 'ocean'
Lake

Maraja- 'made of the sea'
Maris- 'of the sea'
Marinus
Maya- 'water'
Meltem- 'sea wind'
Meraud- 'sea'
Meri- 'sea'
Mira- 'ocean'
Moana- 'ocean'
Mortimer- 'still water'
Muirgel- 'bright sea'
Muirgen- 'born of the sea'
Marilla
Marina
Marlowe
Misty
Maxwell

Naia- 'wave'
Nanami- 'seven seas'
Nereida- 'water'
Nereus- god of the sea
Nerina
Neptune
Nile
Noelani- 'heavenly mist not found on earth'
Nomvula- 'mother of the rain'

Ona- 'wave'
Ocean

Pelagia- 'sea'
Pearl
Pule
Pavati- 'Crystal clear water'

Rio- 'river'
Rosemary- 'dew of the sea'
Rain
Reef
River
Ronan
Reva

Squalos
Sæwine- 'sea friend'
Sarasvati- river goddess. 'Possessing water'
Sevan- 'lake'
Shannah- 'slow moving water'

Tasi- 'sea'
Tiamat- 'sea'
Tirta- 'sacred water'
Talulah
Talia-'dew water in the form of droplets of heaven'

Undine- 'wave'

Vapos

Waverly

Yam- 'sea'

Earth:
Avani- 'earth'
Amber
Arden
Adam- 'son of the red Earth'
Aaron- 'a high mountain'

Bhumi- 'soul.' An earth goddess
Briar

Canyon
Clay
Clarimond- 'sunshine of the earth'

Duster
Diana
Demeter- 'earth mother'
Dahlia
Daisy
Dion- 'son of both the heaven and the earth'

Eardwulf- 'land of the wolves'
Eden
Elowen
Everest
Eve
Ela- 'earth'

Fern
Flora
Forrest
Forest
Fauna

Gritt
Graund
Gaia- 'earth'
Glenn- 'nature'
Greene

Hazel
Heath
Hailey- 'a meadow'
Hermione- 'messenger of the earth'

Ilesha- 'earth lord'
Isla- 'island'

Jasmine
Juniper
Jasper
Jahan- 'earth and the world'

Ki- earth goddess
Kaj

Lambert- 'bright land'
Laurel

Meadow

Nirvana

Oak

Papa- goddess of the earth
Pierre
Peter- 'stone'

Riku- 'land'
Roland- 'glorious land'
Rocky
Ridge- 'narrow elevation of a mountain'

Savannah
Stone
Slate
Sena- 'beauty of the earth'

Terbis
Terra- 'earth'
Tlalli- 'of the earth'
Terran

Violet
Vale- 'valley'

Willow
Wekesa- 'someone who was born during crop-gathering time'

Author's Note: I apologize for the short list, but I hope it helps. I also decided to divide these by element rather then gender to make things easier. Many of the names are unisex as well. Thanks for reading, and leave a vote if this helped!