Different strokes for different folks. I live my life in a way that I want and do not apologize for it or care to hide it.
I wouldn't want the job if they would discriminate against me for something that I do/am/support.
Actually I rarely apologize or hide things to people I communicate with in person and online...so I guess its like more about having control of what one can search on you. Also sometimes its useful to not reveal certain things in certain situations.
Also its a bit crazy, but I imagine research companies searching your name and finding data etc. not necessarily bad, but I like my life to remain a little up the imagination of people I don't even know...and I don't care to provide info for any info. gathering that may be going on.
Also sometimes if its a good job or a contract offering excellent pay, who cares if whoever hired you is an asshole, lets say some guy didn't hire me cause I have pics of me at the weed march, and he's one of those weed paranoids, he searches me and then he sees those pics and decides to hire some other prick. So just by not revealing information you can make your money and move on.
Another way to look at it is if you were hired by above mentioned sample, the weed paranoid boss, and you complete your contract and do great work, the boss is happy, then you can reveal info. ie. "by the way I had fun at the weed march"...and he may think "hmmm, maybe I should not discriminate so much"...or if he has a real pickle up his backside...he will get annoyed, you got good money and on top of it either pissed this boss off (fun)...or he used his brain more (cool)....
Perhaps I am over-thinking this but thats why it can be useful to not always use your real full name online.
Or if you think about it its useful in other situations/not online.
For example lets say some girl worked as a nude dancer to make money for college. This is a good time to use a fake name. I knew a girl like that actually, and she made very good money and then went off to college, she was broke/poor before.