Some people shy away from that question, usually because they do not want others to think they have an ego; after all, the practice itself is called ego surfing, or even vanity searching, because of the assumption that you have to be vain to search for yourself online, but it’s actually really important, especially if you’re an author or an artist and have published copyrighted content.
Personally, I google myself on a weekly basis. I search for my name, my aliases, my published novels, my to-be published novels and even the fanfiction stories I wrote many years ago. I’m not ashamed to admit it. My work is important to me, and I want to make sure that nobody is abusing it or using it for their own personal gain at my personal expense. Plus, occasionally you may come across something nice that you hadn’t been aware of before… a little mention here, a little compliment there, a review you never noticed… it’s all pretty interesting.