From a surname that was from a place name: either Annesley in Nottinghamshire or Ansley in Warwickshire. The place names themselves derive from Old English anne “alone, solitary” or ansetl “hermitage” and leah “woodland, clearing”.
Means “the only one” in Finnish. In the Finnish epic the Kalevala this is the name of a girl who drowns herself when she finds out she must marry the old man Väinämöinen.