Because I'm a mythology geek :)
Also you're free to ask which gods the Pokémon correspond to

Name: Braviary
Species: Braviary
Gender: Male
Type: Normal/ Flying
Special features: None
Personality: tough, brave, stubborn, reckless
Backstory: He was found caught in a snowstorm on top of a mountain
Adopted by: kinata_dreamnia

Name: Mocha
Species: Miltank
Gender: Female
Type: Normal
Special features: None
Personality: sweet, patient, loving (like the opposite of Hera in the PJO series OHH)
Backstory: She was found as an egg in an empty pasture
Adopted by: ThisLlamawantsDrama

Name: Rocky
Species: Mudsdale
Gender: Male
Type: Ground
Special features: None
Personality: uptight, judgmental, adaptable
Backstory: He was found attacking a Team Skull Grunt
Adopted by: Dalice-Knox

Name: Poppy
Species: Tepig
Gender: Female
Type: Fire
Special features: None
Personality: playful and curious
Backstory: She was found batting at autumn leaves
Adopted by: NightWolf531

Name: Lyreaus
Species: Seviper
Gender: Male
Type: Poison
Special features: None
Personality: mean, cruel, selfish
Backstory: He was found stalking a Pachirisu
Adopted by: @ThePandoriac

Name: Nocturne
Species: Noctowl
Gender: Female
Type: Normal/ Flying
Special features: None
Personality: smart, wily, persistent, determined
Backstory: She was found flying above the clouds at night
Adopted by: FrostedAurora