It actually took me a few months to get my site to rank #1 for its own brand name. It was extremely frustrating, but I worked at it and it has paid off. Now my brand name and other related terms are by far my top search terms, and this is on a site that gets 75% of its traffic organically from search engines.
For your own name that can be pretty hard if it is a common enough name.<p>Alex Blom probably will do just fine (it does, I checked), but John Smith would have a much harder time of it, even John Smith the greengrocer.