I think the answer is different for everyone! What's right for one may not be right for another. I decided to stay quiet about it. Only my husband and one of my best friends (who lives across the country) knows. I'm a private person to begin with, and I don't like much attention, so I knew I didn't want to share this with many people. I may share with other close friends in time, but not yet.
Although two in my family have had WLS, and several family friends have had WLS, my family members are notorious gossip lovers. "So-and-so looked before before WLS; he looks sick now!" - "Can you believe she took the easy way out?" - "I hate who she's become since WLS!" and on and on. Being around that negativity prior to my surgery made me determined not to share. I opted not to tell anyone at work, either, because I felt it might make others be more judgmental of what goes into my body. (Probably just my own paranoia, but still!)
Here are two things I read on this forum that really helped me come to terms with my decision, and may help you, too.
Take your time and make sure you feel good about your decision before sharing. You can never un-tell someone, but you can always change your mind and share later.
WLS is one of the only surgeries where we feel like we are being "deceptive" if we don't tell. But we wouldn't necessarily shout a gallbladder surgery from the rooftops. It's OK not to share!
Best of luck to you!!