Amy & May
The names are anagrams of each other

Cara & Mia
In Italian Cara means “beloved” and Mia means “My”, together they mean ” my beloved”, caramia

Chandra & Selene
Chandra mean “moon” in Sanskrit, and Selene was the Greek godess of the moon.

Columba & Jemima
Both names mean “Dove”, in Latin and Hebrew respectively

Daphne & Laura
Both names mean Laurel, in Greek and Lain respectively

Deborah & Melissa
Both names mean “bee”, in Hebrew and Greek respectively

Dorcas & Tabitha
Both names mean “Gazelle”, in Greek and Hebrew respectively

Dorothy & Theodora
Both names are formed from Greek elements doros “Gift” and theos “God”, but the elements are in different order.

Elijah & Joel
The Hebrews had two name elements meaning God, these names contain both, but in different order

Erica & Heather
Erica means “heather” in Latin 

Ezra & Ophelia
Both mean “help”, in Hebrew and Greek respectively

Ione & Violet
Ione, means “violet” in Greek

Ira & Ria
The names are anagrams of each other

Irene & Salome
Both names mean “Peace”, in Greek and Hebrew respectively

Johan & Jonah
The names are anagrams of each other

Jonathan & Mathew
Both names from Hebrew elements yehu, “the Lord” and matis, “gift”, but the elements are in different order.

Lucius & Uri
Both names mean “light”, in Latin and Hebrew respectively

Mary & Myra
The names are anagrams of each other

Melanie & Phoebe
Both names are Greek, but Melanie means “dark”, and Phoebe means “Light”

Reva & Vera
The names are anagrams of each other