It's the other way around anyway. More people are actually atheist than would self-identify as such. It's still too socially uncomfortable for a lot of people. Some will straight up fake like they have religious faith and believe in God when they really don't.
Others can even admit that they don't really believe, but still perform some kind of mental gymnastics or semantics game to avoid deeming themselves atheist because it still feels like a nasty word to lots of people.
In America there are still plenty of communities where being openly atheist will make you a pariah. As eynon pointed out, there is less cultural/social pressure these days to actually attend church, but that still doesn't mean people are going to come right out and admit that they're atheists.