I don't think I have met an
Angela or
Angie with red hair, but I don't see why it couldn't work. I have met blonde and dark haired Angelas; I don't think of a specific hair color when I hear the name.
Based on the description of the character, I think
Angela would be perfectly fine.
Laura would also work well for her.
Other ideas:
Andrea - I used to know an
Andrea with red hair.
LilySarahRebeccaErinLaurelLaurie /
LoriCarrieKerryCallieKellyAnnieAnnaHannahCarolineVictoria