Without accounting for stereochmistry, which is partially ambigous in this drawing, I would dare call it(numbered clockwise): calling "X" bromine, because I dislike being ambigous (2-halo, nah!):
1-bromo-3,4-methylenedioxy,6-bromo, 8-methylamino, non-1,3,5-ene
As for stereochemistry, the 1,2 double bond is drawn trans, but the one at5,6 is not drawn in a conventional way, the bond angles could't bee like that. Perhaps it's a limitation of 2-D drawing, but none the less it's ambigous. If I had to guess, I would draw the halogen straight down, rather than up, but there could be many arguements deepending on the previous chemistry.
Without the hydrogen at position 8, One cannot call it an R- or S- stereocenter, though I guess If I get off my lazy ass and look up Rhodium's references, I could figure it all out from the reactions, but, hey, I just wanted a crack at practicing my nomenclature.
yours truly,
1,3,-Boz-8-yne