I had to get rid of my blog, because of my employer, so I deleted it. But when I Google for my name, the first thing that pops up is my blog, and my profile.
Deleting your blog, as I've written before, needs to be done with care and forethought. If your blog is cached, the cache has to be managed properly, before the actual blog contents can be removed from the blog host (ie, Blogger).
You can manage your blog's cache, in the Google search engine, using Google Webmaster Tools. If you just deleted your blog, this won't be possible. You're going to have to re publish your blog, add it to Google Webmaster Tools, then use the Google Webmaster Tools "Remove URLs" wizard to instruct Google to remove it from their cache. This is just another detail that you should consider, before deleting the blog in the first place.