I dunno what White/Cheren is yet, but how about:
MessyRoomShipping - might be unspecific since battling both Bel and Cheren messes up the PC's room
BelarusianShipping - female PC is called White by fans; Cheren's name comes from the Russian word for black; the country Belarus gets its name from Belorussia or White Russia. Considering that, this could actually be Cheren/Bel instead since the word is Belarus...
EasternBlocShipping - failing BelarusianShipping... Cheren comes from the Russian word for black, but Black is already a name given to the male PC. Russia was an Eastern Bloc country. I was about to go for pun with EasternBlackShipping, too.
CheckmateShipping - this sounded too cool to not be used for something regarding BW. Mate = friend, checkmate relates to chess, black and white pieces, etc.
Well, I tried.