Deleting one object, not all objects at once.

I have a script that deletes an object that is called a certain name "Object 1" when it is clicked. I have the script attached to all of my gameobjects and it works fine. I can click every other object and it doesn't trigger the deletion. As soon as I click the object that should be deleted, it deletes ALL of my other objects with the script attached. Here is my code for deletion:

 if(Box.collider.gameObject.name == "DeleteMe")
 {                        
 Destroy(this.gameObject);
 }
 else
 {
 }

I have tried using this.gameObject and just gameObject, it still deletes all objects with the script attached to. I'm using c#, if anyone could help it would be great thanks. I'm new to unity so excuse if I've made a stupid error!