As a rarer (but older) masculine name it is probably derived from a surname: see Fay 1 or Fay 2.
As an Armenian name, it might possibly be a diminutive of Yevgenya.
Lastly, in addition to all of the aforementioned, the name Fenya could possibly also be the Armenian and Russian form of the Greek given name Fenia.
A known bearer of this name was Fenia Chertkoff (1869-1927), a Russian-Argentine educator, feminist and political activist. Please note that Fenia is a variant transcription here: her original name would have been either Феня (Fenya) or Фения (Feniya).
This spelling was used by Lord Byron for characters in The Giaour (1813) and Don Juan (1819), and it is through him that the name was introduced to the English-speaking world.
Though in use elsewhere in Europe, the name was very rare in the English-speaking world until the 19th century, when Queen Victoria began her long rule of Britain. She was named after her mother, who was of German royalty. Many geographic areas are named after the queen, including an Australian state and a Canadian city.