I'm curious as to what Vince does actually own regarding rights to Hogan's stuff.
Not an awful lot actually, it seems that Hogan was able to trademark almost everything related to his gimmick throughout the years. The only thing he couldn't trademark was the "Hulk" part of his name, which was disputed by Marvel, although they eventually settled on a fair use policy with each other.
Vince does own 90% of Hogan's career on tape as WWE has accumulated almost all footage from AWA and WCW (two no longer active companies that Hogan had worked prolifically for). Vince also owns the rights to the nWo including presumably, the Hollywood Hogan attire.
The name "Hollywood" originally came into play during Hogan's dispute with Marvel over the "Hulk" name. Following Hogan's heel turn and his joining of the nWo - he adopted it as part of his name in order to differentiate his face character (Hulk Hogan) with the heel character he was now portraying ("Hollywood" Hulk Hogan or Triple H

I'm not entirely sure if Vince has ever contested the trademarks to Hogan's gimmick. It was Vince himself - and his fascination with Irish names, that came up with "Hulk Hogan". Before WWF, Hogan went by Sterling Golden or Terry Boulder.