Even the name "Rescue" always sounded kinda lame to me. Like what is she supposed to be? A superhuman paramedic or something?
To be fair, it is one of the very few superhero names that isn't essentially a self-aggrandizing brag. Iron Man, Superman, Captain America, Captain Marvel, Ms Marvel, Mister Fantastic, Daredevil, etc, are all variations on, "I'm friggin' AWESOME!"
Rescue, though, is nothing but a humble mission-statement. It's a name that says, "I'm just here to help" and was probably designed specifically as a contrast to the self-aggrandizing names of the vast majority of superheroes. It's so humble that it's barely a name at all.