Hey! random Godot citizen here, I hope I can be of some help.
If I understood correctly, what you are trying to achieve is to change the text of the labels of a certain group, if any of them is changed? Like this:
A label's text was changed.
Update all the labels in that same group so they all have the same(or some other) text.
End of Pseudo Code
If that's the case then I could recommend using custom signals.
What really confuses me is that you are storing the labels inside the groupName array. How do you know which label is which? Maybe groupName isn't the one you think it is, and that's why it isn't printing the correct text.
Again all of this is my guessing. Maybe if you share another example, we can provide a better solution.