nanomania - From what i can see there is major tissue loss in the tips where the white stops and the brown sticks are in. You can see in other spots where it seems the calcium skeletons are showing through. if you bought that sea fan in the condition show in the picture - you may want to take it back (imo). It will be a bit of a challenge to turn this coral around (sorry just my opinion).
I haven't ever heard of a white sea fan to be honest. But if they have zooanthellae algae - ususally they should have some colour from the algae. If its a colour morph its probably pretty rare.
Not to be picky but that looks more like a straight gorgonian from the growth pattern.