private bool check(string str){
 return str.EndsWith("xxx");
}

Predicate<string> predicate=new Predicate<string>(check));

private void OpenMenu(GameObject gob){
 Predicate<string> predicate=new Predicate<string>(s =>s.StartsWith(gob.name) );
 int i=_nameList.FindIndex(predicate);
}

Predicate<string> predicate = s => s.StartsWith(gob.name);

int index=_nameList.FindIndex(s => s.StartsWith(gob.name));