It is actually called a vanity search and so many people are surprised by what they see. If you have a LinkedIn profile, Twitter account or a Facebook page I would bet you they are on the first page of the results. Is your website on the first page? Due to the heavy traffic of the social giants they will show high but your goal should be to have your website on the list as well.
Another thing you should learn by doing this is all the other places you show up. Are those websites telling your story you want told? Are you able to edit any of these websites? Try to optimize the data on those sites if they are going to come up high for your name make sure any profile information points back to you and your website.