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.
As an English name it has been in use since the Middle Ages, originally in the form Clare, though the Latinate spelling Clara overtook it in the 19th century and became very popular. It declined through most of the 20th century (being eclipsed by the French form Claire in English-speaking countries), though it has since recovered somewhat.
This is not the usual spelling in any of the Scandinavian languages (in Sweden and Denmark it is Freja and in Norway it is Frøja) but it is the common spelling of the goddess's name in English. In the 2000s it became popular in Britain.
This name also appears in the New Testament, belonging to man who sheltered Paul and Silas. In his case, it may represent a Hellenized form of a Hebrew name. It was not used in England until after the Protestant Reformation.
In England, it began to be used as a given name after the Protestant Reformation. It was moderately common in the 19th century. It began to rise in popularity again in the late 1980s, probably helped along by characters on the American television shows Friends (1994-2004) and Charmed (1998-2006). It is currently much more common in the United Kingdom, Australia and New Zealand than the United States.
A moon of Saturn bears this name, in honour of the Titan.