I am looking for a way to find a script, that is positioned under the same GameObject, but not in the same hierarchy. Since there is more GameObjects with the same name and the same Script, "find" is not a possibility. I have been looking through the documentation for a sollution, but haven't been able to find anything..My apologies if there is something after all. My glasses might need cleaning ;)
Uh... are you looking for Object.FindObjectOfType? This returns the first instance of whatever component you give it, but be warned, it is slower than GetComponent and friends!
Edit: If you want to find a child component in a different game object, you first need to get its reference. See this post for how to access other game objects and obtain their references:
http://unity3d.com/support/documentation/ScriptReference/index.Accessing_Other_Game_Objects.html
After you have a "`GameObject`" object, you can just call `myObject.GetComponentInChildren()` to get the component reference in that particular game object.