Alecto is a Fury (Erinye) in Greek mythology, the punisher of moral crimes. Since Furies have serpent hair and are known to be quite ugly even though I actually like what they stand for and how pro-women they are in the Oresteia, due to the negative connotations I wouldn't name my child this. She's also a Death Eater in Harry Potter 7.
I love the sound, and it makes me think of a powerful young woman with a lot of influence. Unfortunately, it also makes me think of Alecto Carrow from Harry Potter, but since she barely gets a mention in the movies and few people read books these days I think this association is obscure enough that most wouldn't get it.