CAWEvo, If you look at the area, theres not enough room for Barbed Wire thats why it's barb wire and lights instead of lighttubes.
Besides there is no correct answer that I could find. if you go to http://www.hardcorehomecoming.com
and click on media it says "Funk gets cut out of the BARBWIRE!" and "Dramatic No-Rope Barbwire Entrances", Etc... So thats three ways. Barb Wire, Barbwire, Barbed Wire. So who knows.
About the battle royal part. I know it's called Endless in Japanese but personally I think it's a bad name. Endless means never ends but the match does end at a point. And it is too long to put eliminated wrestlers never leave so I figured SWA Rules would do.