We do a Secret Santa, in my housing, and honestly I don't think anyone pays any attention to other people opening their gifts. this is just how we do it, the gifts are distributed to everyone and everyone opens their gifts at approximately the same time. So no one is in the spotlight. This might not be true for you, depending on how your work does it, but I do think people are much more interested in their gifts than in watching other people.


And as has already been said a big smile, and a thank you once you've opened it will go a long way. People may ask you what you got. It's ok to just hold it up to show which might be easier than talking if your anxious and saying something like "isn't it great"