This is not a legal issue, it is a Blogger procedure question. You need to get your password reset and then delete the blog. This is a simple process once you have your password retrieved. I prefer WordPress and have never had any problem doing this with my blogsite. If you are meaning a blog post on someone else's site then that is up to the blog owner, so I take it you are talking about your own blogsite.
I am not your lawyer and you are not my client. Free advice here is without recourse and any reliance thereupon is at your sole risk. This is done without compensation as a free public service. I am licensed in IL, MO, TX and I am a Reg. Pat. Atty. so advice in any other jurisdiction is strictly general advice and should be confirmed with an attorney licensed in that jurisdiction.
Echoing the other answer, you should follow the policies set forth by Google for a "lost password." They will need, one way or another, some way acceptable to Google, to verify that you are indeed owner of the account. Once you do, then I assume you can do it yourself. Note, however, that there may be some "persistence" in their search results of items from your blog, assuming that it was indexed. They are quite persnickety about removing search results "before their time..."