You can do that with some custom js.
Add this to your custom js (in the form you are printing):
var selectedTabName = "";
setTimeout(function(){
selectedTabName = jQuery(".tabSelected").text();
jQuery(".tabBase").on("click", function(){
selectedTabName = jQuery(".tabSelected").text();
});
},1000);
and this to the Print header field:
Current tab name: {var:selectedTabName}
Alexander