Up until June 23, it will be possible to fly without showing ID. I didn't know this and you probably didn't either because it isn't something well publicized and goes against all the signs at the airport informing fliers to show ID.
I would use a fake name if I could. Why? It doesn't mean I'm a terrorist, it just means I want privacy and don't want my name entering some government database that datamines for information. Or being tracked. I don't want anyone not in my circle to know where I am. Why? It's nobody's business, that's why.
And really, what real security is added by checking a name? I'm sure a well-funded terrorist could get some genuine looking falsified documents and book his or her flight under a pseudonym.