How not to call the Find () method of the same Gameobject in different classes?

How to simplify? Can it be called once and saved as a variable or constant?

yes you can save it in a var like this and access with a reference to that class instance.

public GameObject YourObject { get; set; }

void Awake()
     yourObject = GameObject.Find("name");

if you want to access it without a reference to the object (commonly thought as global but is really global) yoou can make it static, but only when it makes sense.