If a search under your specific name turns up nothing then Google hasn't "seen" your website yet. The best way to fix this is get other sites to link it, Google gives a lot of "weight" to the number and quality of sites linking in to yours.
Look for directory sites that will link you for free, or pay for some ads. A link from www.dmoz.org is important (but this really does take ages)
The more sites linking to you the better, and the quicker google will find you (think 6 months is an over estimate btw), you could even do a link from this thread
I'd work on your content and make sure you have lots of relavant keywords. If you read up a bit on SEO there's lots you can do but it takes a while for the search engines to pick up new sites/changes etc.