As an English name, Chloe has been in use since the Protestant Reformation. It started getting more popular in the 1980s in the United Kingdom and then the United States. It was the most popular name for girls in England and Wales from 1997 to 2002. This is one of the few English-language names that is often written with a diaeresis, as Chloë.
This is also an alternate transcription of Russian Ева (see Yeva).
Despite this potentially negative association, the name was occasionally used by Christians during the Middle Ages. In the English-speaking world both Eve and the Latin form Eva were revived in the 19th century, with the latter being more common.
The name was not used in England until after the Protestant Reformation. A notable bearer was Martha Washington (1731-1802), the wife of the first American president George Washington. It is also borne by the media personality Martha Stewart (1941-).
As an English name, Zoe (sometimes with a diaeresis as Zoë) has only been in use since the 19th century. It has generally been more common among Eastern Christians (in various spellings).