Call image in pre composition by name with expression

What you want is not possible. A pre-composition is always just an instance of the same comp and responds to the same changes globally. Even all Essential Graphics/ Master property trickery doesn't change that. You have to use a different workflow like staggering the images and accessing them via time-tremapping, which then could be rigged with a valueAtTime() expression or even a simple slider. Similarly, you can use all sorts of effects to "unhide" layers by rendering them inside the effect while it's otherwise invisible by referencing the effect in one of the effect's input dropdowns. This then again could be controlled with expressions. Either way, your original idea will never work and even in the scenarios I laid out you can't avoid duplicating the pre-comp at least occasionally.

Mylenium

I'm not sure what you're asking, but if you do something like this:

myLayer = null;
try{
  myLayer = comp("My_images").layer("a.jpg");
}catch(e){
  try{
    myLayer = comp("My_images").layer("b.jpg");
  }catch(e){
    try{
      myLayer = comp("My_images").layer("c.jpg");
    }catch(e){
    }
  }
}

at the end, myLayer will be a.jpg, b.jpg, c.jpg, or null (if a, b, and c don't exist). Does that help?