If I understand your question correctly, it seems as though you can do this with a text field right above your tab control rather than trying to change the tab names.
Just put the another copy of the field that you use with your radio button over the tab control but leave it as a text field instead.
That's my fallback and how I have it set up now. But having them as the tab itself would be great.
I can put the radio button field inside an empty tab label, and it works fine -- but only if that tab is selected.
I am not sure what "the results of a radio button" means, but you can put any object (incl. a field) in a tab header - you just need to do so as many times as there are tabs (you'd probably want to use two versions of the same object - selected and deselected).
One way to control the exact placement of the object inside an unselected tab is to select it by marquee, then nudge it into place using arrow keys.