Just to mention that as an English name, Angel was used for both sexes even before modern times. An interesting book called 'Curiosities of Puritan Nomenclature', available online, shows that Angel/Angell was occasionally used in England to the close of the 17th century (but not by Puritans). For instance: “1682, April 11. Baptized Angel, d.[aughter] of Sir Nicholas Butler, Knt.”.
Derives from the Greek name: ΑΓΓΕΛΟΣ, = messenger, also called like this the heavenly creatures in white wings. Verb: ΑΓΓΕΛΩ = to send a message, to tell Noun: ΑΓΓΕΛΙΑ These words are spoken in everyday contemporary Greek.
Angel is derived from Angelos (Greek) or Angelus (bells) is a very old name that dates back to being given in medieval times. It is by no means a trendy name but rather a name handed down in proud Christian families. It is very much a male name and different countries pronounce it in different ways and use accents. There are many people who give their child a name because it sounds nice without any research into it, and it may be inappropriate then.
An ancient Greek name, "Angelos", same for both feminine and masculine. In Greek mythology, Angelos was one of the epithets of god Hermes. Also Angelos was a daughter of Zeus and Hera.