Linking object functions

You could for example store the list of the objects in a script and when you need to get another random object use a function from there.

For example:

 using UnityEngine;
 using System.Collections;
 using System.Collections.Generic;
 
 public class ObjectsList : MonoBehaviour {
 
     public static ObjectsList instance;

 // Drag all the available objects here from hierarchy panel
 // or else use FindObjectsOfType<YourScriptName>() in Awake or Start
     public GameObject[] allObjects;
 
     void Awake () {
         instance = this;
     }
     
     public GameObject GetRandomObject (GameObject excludeMe) {
         List<GameObject> list = new List<GameObject>(allObjects);
         list.Remove(excludeMe);
         return list[Random.Range(0, list.Count)];
     }
 }
 

Then in your script attached to the object you'll call the following line and apply your rotation or everything else to it:

 GameObject randomObject = ObjectsList.instance.GetRandomObject(gameObject);