I use different handles for this site (though I use this one on one other site), Twitter, and Instagram. My first name is on the latter two sites, but not my last.
When I was dating online, I used another screenname altogether. I signed some messages with my first name once we were getting ready to meet.
I do use first name and last initial on Yelp, but I haven't written any reviews since moving to my new home because I didn't want a few people familiar with that account to find me for at least a while.
Searching my first and last will find my LinkedIn and my semiprofessional blog and writings for my graduate program.
My Facebook has my first and last name on it, but it's not google-able. I post all sorts of things on there, but my life isn't too wild anyway. I know all but 2 or 3 of my "friends" personally, and when I found out that some distant relatives were sharing information about my life with my father who I've given the cut direct to, I defriended and blocked them. I link my Instagram to my Facebook; I believe I've also shared tweets on there, but not in a long time. I have real-life friends on both accounts.
Our task is to set up a presence we're comfortable with, and to share or not share it with others as we are comfortable. I try not to link anything to my real identity that I would be embarrassed about or that might create complications in 'real life.'