Atheism is not a religion. And so, it really isn't an appropriate response to "What's your religion?" If someone asks you this question, and you say "atheism," you are strengthening inaccurate views some religious believers hold that atheism is a religion. But atheism is not a religion. I suppose you could say, "None. I'm an atheist" if you wanted to be accurate and still identify yourself as an atheist.
I was in the hospital recently, and I was asked this question. Needless to say, it really freaked me out. My response was, "I don't have one." I was sufficiently out-of-it when I provided this response that I think it is fair to say I didn't put any thought into it. It was more like I heard myself saying it and only realized what I was saying afterward. Had I had more of my wits about me, I might have said something very different. I might have even lied and said, "I'm a Southern Baptist just like you." Although I was treated well, a response like this might have resulted in my being treated even better.
I have heard many atheists rail against being asked this kind of question at all, and I can certainly understand where they are coming from. There are some contexts where it seems so incredibly inappropriate. It seemed inappropriate to me in the hospital. At the same time, I do understand the rationale for asking it in at least some settings. Whether we want it to be true or not, religious belief is important to most of our neighbors here in the U.S. I share the hope of many atheists that this will continue to decline and even that it will decline at a much faster pace, but I know that is going to take time. For now, I have to think that there are very few of us (especially where I live) who would be bothered by such a question. Most of my neighbors would probably welcome it as an invitation to talk about Jesus.