Hey @membermarketing 
If you mean you want a text or formula column to automatically output the name of the group it is in, this is not possible.
However, if you have a specific Status Column to show the group an item is in, you can use Automations like these to set and change the status according to the group it is created in or moved to:
I hope this helps! Remember to mark as solved if this answers your question 
Cheers,
Jenna