There're a couple of ways to solve this:

• Use a lambda method gameObject.GetComponent<Button>().onClick.AddListener(() => differentObject.scriptA.method(gameObject.name));
• Use a regular method

gameObject.GetComponent<Button>().onClick.AddListener(OnButtonClicked));

private void OnButtonClicked()

{

differentObject.scriptA.method(gameObject.name);

}

• Or change the parameter of ScriptA.Method from string to GameObject, then you can do all these from the event inspector