A vibrant variation of Adele, with a bit of extra flair from that "-a" ending. It could join the army of popular A girls' names, especially with its tie to the success of singer Adele. 
 Adela, which came to England with the Normans in the eleventh century, has a royal pedigree via William the Conqueror's youngest daughter.
 Adela Quested is a character in E. M. Foster's novel A Passage to India, and the name also appears in an Agatha Christie story. Journalist/novelist/screenwriter Adela Rogers St. .Johns was a colorful character in Golden Age Hollywood.
Adelia is another appealing variation, an alternative to the rising Amelia, and entered the UK Top 1000 in 2022.

Adela

Adelais

ADELISE

ADELIZ

Adeliza is a unique member of the popular Adelaide-Adeline family. Different enough to distinguish it from all the others? Maybe, and it's definitely got an appealing sound that makes it sound a bit like a smoosh of Adele and Eliza.

Adeliza

ADRIANTJE

AELFLAED

AELIS

AENOR

ALASIA

ALBERADE

ALDONZA

ALFAISE

ALFFLAID

ALFGIFU

ALFTHRYTH

ALIANORE

A chic and sassy French choice, popular in France but likely to be confused with the more prosaic Alex in English-speaking countries. Although sometimes used in the US as a variant spelling of Alex, the French name Alix actually derives from a medieval French form of the name Alice or Adelaide. 

 Several members of European royal family have borne this name, including Alix of France; Alix, Duchess of Brittany; and Alix of Hesse, Empress consort of Russia. More recent are Alix d'Unienville, WWII spy; Alix Kilroy, one of the first British women to become a public servant; and engineer Alix Pryde.

Alix

ALPAIS

ALSWITHA

AMABILIA

AMABILIS

Amice

ANGHARAT

ANKARET

Annora is a noble name, a distinctive twist on its most essential form: Honor. Other variations to explore include Honora and Nora. 

Annora

Aoife, pronounced EE-fa, is derived from the Irish word aoibh, meaning "beauty." Aoife was borne by several different heroines of ancient Irish legend. In one tale, she was the fiercest woman warrior in the world and enemy of her twin sister, Scathach.
 
Aoife is very popular in Ireland, and is catching on across the UK as well. Aoife is sometimes Anglicized as Eva, but the names are from independent origins. Eva shares roots with Eabha and Aoibhe, both also currently popular in Ireland.

Aoife

AREMBURGE

AUPALS

AURENGARDE

Aveline is a name that's long been an obscure cousin of more widely-used choices, but may come into its own riding the tail of the megapopular Ava, which may derive from the same root.

 Although Aveline is a cognate of the French word for "hazlenut", the name actually derives from an obscure Germanic root, the meaning of which is not clear. Theories include "desired, wished for" and "water, island".
 
Aveline is different enough to sound distinct, but be warned: You will forever be explaining that no, it's not Adeline, not Evelyn, and so on.

Aveline

BARENGARIA

BAVA

Benedicta

BERSWINDE

BERTILA

BERTRADE

Long forgotten Old Testament name with modern potential. 

Bethia

Bethoc

CINNEGUNDE

Clemence

Pronounced klo-TEELD, this name is well used in France, but rarely heard here; it has a chic and sophisticated air.

Clothilde

Constance is one of the more subtle of the virtue <a href="https://nameberry.com">baby names</a>, but still has quite a prim and proper image. One impediment to its revival has been the decidedly dated nickname Connie, though modern parents might well opt for using the strong and dignified name in full.
 One of William the Conqueror's daughters was named Constance, and in Shakespeare's King John, Constance is the devoted mother of King Arthur. Constance was widely used in the seventeenth century by Puritans: Constance Hopkins was a young passenger on the Mayflower.
 The fictional Constance Billard School appears in TV's Gossip Girl, and Constance was the first name of the decidedly non-prim and proper Lady Chatterley.
 Oscar Wilde's wife was Constance, and Mozart's spouse was the German form Constanze, nicknamed Stanzi.
 Though Constance has been neglected here for a number of years, it's still ranks at Number 120 in France.
 Trivia tidbit: Constance was the birth name of 1940's peekaboo-hairdo star Veronica Lake and also, not surprisingly, Connie Britton.

Constance

Constancia

CRESTENE

CUNIGUNDE

In the New Testament, Damaris was an Athenian woman converted to Christianity by St. Paul. Known for her charitable work, her name was a favorite among the Puritans. Having slid off the bottom of the Top 1000 in 2012, Damaris might be deserving of more attention by parents in search of a New Testament name that is unusual but accessible, especially since girls' names ending in 's' are coming back into fashion. 
 Damaris is a supermodel name via Damaris Lewis; it's currently a Top 100 name in Chile.

Damaris

DAME

DANGEROSE

DARBFORGAILL

Dema

DEVORGILLA

DOBRONEGA

Popular Portuguese and Spanish name that refers to "dulce nombre de Maria" -- the sweet name of the Virgin Mary. English variant Dulcie has a different pronunciation.

Dulce

DYDDGU

NerdyNamer's list "Unusual Female Names From My Genealogy A-D" of 55 great name ideas: Adela - DYDDGU!

Unusual Female Names From My Genealogy A-D

Interesting and unusual names from the female side of my family tree from the year 602-1983 A-D