hannahmadison's list "Faves" of 2 great name ideas: Imogen - Ajax!

Faves

Imogen has long been fashionable in England and is gaining favor in the US among stylish parents. Pronounced the British way — the initial i is short as in Kim, as is the final E as in Ken — Imogen is as pretty and classy as it is distinctive.
 
Though never in the American Top 1000, Imogen may be more popular in your hip neighborhood than that statistic would suggest. A contemporary classic in England and Wales, Imogen has ranked in the Top 100 ever since detailed naming records began in 1996. It's also a Nameberry favorite, consistently among the Top 100 most viewed girl names on our site.
 
The story goes that Imogen originated as a Shakespearean printer's misspelling of the traditional Celtic name Innogen, used by him for a character in one of his last plays, Cymbeline. The Innogen of legend, who Shakespeare’s character was based on, was the wife of Brutus of Troy, the first king of Britain. Earlier versions of her name, including Ennoguent, Innoguend, and Innoguent, were found in Brittany from the 9th-11th centuries. They are probably derived from the Gaelic word inghean, meaning "daughter" or "maiden," and possibly have a connection to the Proto-Celtic word for "white," from which the suffixes -gwyn and -gwen evolved.
 
Even if Shakespeare did happen upon Imogen by accident, he wasn't the first person to use the name. The Latin name Imogenis, meaning "lowest-born," existed centuries before Shakespeare, and was first recorded in the 13th century.
 Imogen gained attention in recent times through its link to Grammy-winning musician Imogen Heap. Other pluses: Imogen has the wonderful namesake photographer Imogen Cunningham and also a meaning that can't be topped. Immy is the cute diminutive; in the book and movie Fried Green Tomatoes, the character Imogene's nickname was Idgie.

Imogen

Ajax is the name of two Greek heroes, both who fought in the Trojan war and feature in Homer's "Iliad". Distinctive yet familiar in sound, thanks to similar choices like Jack, Asa, and Ajay, Ajax is also the name of a foaming cleanser in the US, and if you find that reference too strong, you might try the shortened Jax instead. 
 
In a recent year, 36 boys were called Ajax in the US.