Badassium

This can be seen in Marvel's The Avengers Prelude: Fury's Big Week Volume 8:

Fury: He's working on a patent for "Badassium," but has encountered several bureaucratic obstacles.

Is there a name for the element Tony Stark rediscovered during Iron Man 2.

No, it's never named in the movies. According to the novelization of Iron Man 2 it's Vibranium but....

this has since been dismissed by Captain America: The First Avenger (released a year later), which shows that Vibranium already existed in the 1940s.

^Screenrant

..and so could not have been reinvented/discovered by Tony Stark

And is it being actively and currently used to power all his suits including the latest nano tech bleeding edge armor mark 50?

It's the basis for the Arc Reactor which powers not only all of Tony's suits but also War Machine, Rescue and the other Iron Legion droids as well as Stark Tower.

The best answer so far is Vibranium. Based on the novelization of Iron Man 2, as well as the fact that it's the first thing that pops up if you google this question. Just because it's proven to have already existed in Captain America, and much later in Black Panther, doesn't mean Tony couldn't ave re-synthesized it in Iron Man 2. Howard Stark says in Captain America that the shield was made with the only known vibranium to the modern world, so it makes sense that he would try to synthesize it himself.