They will look you up based on your Celebrity Club ID. Offers are mailed out randomly, if at all, so the best advice is what Fly and Sail mentioned above which is to call BCC and ask if they have any offers showing for you, also good to ask what they show for points earned towards tier status. There is no guarantee of being notified of anything you might be entitled to with BCC. Is it too late to find out if I earned points? Do you have to do it in person on the ship? Do you not get notified automatically if you do earn one? I am sure I would have spent even more on my Celebrity cruise (as it was longer). I didn’t know about this last time I cruised. When I did, I had enough points for a free cruise. A fellow gambler at the tables let me know and told me to check with the Casino Host.
I enjoy the casino and while at a table on this cruise learned about free cruises for playing. This year we tried Royal Caribbean because we have our young adult children with us. We have previously sailed several times on Celebrity.