A couple of questions for you.
Your info says you are new here. How long has your tank been set up and running? An anemone isn't the best animal to add to any tank less than 6 months to a year old. They like stable conditions and it takes a new set up that long to get stable and stop having algae or bacteria blooms.
I've heard of Haitian anemone and I always thought it was basically the same as a Condy anemone (Condylactis). Is that what you were told this anemone is? BTW, how much did you pay for it? Condys are common and cheap, as in $10 to $15, despite being protected in Florida now.
To my eyes this is a Bubble Tip anemone. And a very bleached out one at that (not good). Codys or Haitian anemones never have the bubble form in their tentacles and almost always have pink or purple tips or are completely purple. But then most Bubble Tip anemones are pink (rose) or green, not white. And they should cost $40 to $80.
Google images for both and see what you think. I've had both and I seriously think it's a Rose Bubble Tip anemone.
As for closing up like yours, anemones are a peculiar animal. They can be very fussy about water conditions, being moved, changes to their environment and such. Not that they are delicate, but they don't deal well with change. This one looks quite stressed (it shouldn't be all white) and has recently been moved to your tank from a store? Therefore I wouldn't be surprised by anything it might do. Personally, I never would have paid money for this anemone. I might have taken it for free to see if I could nurse it back to health. I'm no expert, but I give this one a 50:50 chance of long term survival.
I'd make sure it gets good, not excessive light and try to spot feed it some small shrimp. Best to turn off pumps so the water is still and try to 'spray' some small mysis shrimp or small bits of some other meaty food over it with a turkey baster. The tentacles should hold on to some and then move the food to it's mouth. Whether this is a Haitian or a Bubble Tip, it feeds itself through photosynthesis and collecting food from the water. Don't over feed it. Just every 3 or 4 days until it starts to develop some color, either pink overall or pink tips. Then cut back the feeding to once a week. Give it time, it could take as long as a couple of months to recover. Don't rush things and other than feeding it, leave it alone.
Good luck.
