I also have a button and when I click on it I want to change the name of a subtab (from a client script obviously). Is it possible ? SS2

I think you may need to to reload the suitelet and then change the name based on some condition, you can pass a parameter in the URL in order to know which name you want to use.

@Simon you should be able to do this with jQuery on the page, you can grab the element name and change it

wow. Let me try. Thanks