Another Vader question

In WCW he was "Big Van Vader". Did WCW own that name or did Leon? 

I'm pretty sure NJPW owned the rights to it and WCW was basically using it under an agreement.  

In the WWF he was "The Man They Call Vader" (technically). Was the WWF afraid that LucasFilm would sue them?

I would imagine so.  If there's anyone more litigious with their trademarks than WWE, it's Lucas.  

By the way, Vader is German for "Father", so maybe the "They" the WWF was referring to is a bunch of his illegitimate kids?

Eh, maybe not… 

Wait, so "Darth Vader" literally means Dark Father?  Isn't that a tad on-the-nose even by George Lucas' standards?