When logged in to Blogger, click the drop down by your name on the top right.
You should then see something like I have below (my email is blocked out in purple).
Click on the words Blogger profile. On the top right, you'll see an orange button that says "Edit Profile." Click on that and then the second category, below Privacy, says Identity. This is where you can change your display name to whatever you want (just make sure your professor can identify you, if you are using it for a class).
Here is how to change your name for all Google products (or change it back if you didn't mean to do it):Instead of clicking Blogger profile in the image above, click Account settings. Then you'll see a screen like the one below. I have a profile image in here, I think from when I had Google Plus (that little puppy is now 125 lbs!). Under the image, choose Edit your profile, which is marked with the blue arrow (the purple area is covering up my email).
Then on the next screen, it's kind of tricky because you just click wherever you want to change something. I know it says click on the parts of your profile you want to edit, but it's still odd. When you click on your name, you will get a screen like the one below where you can change your name.
If you change it here, Google will warn you that name changes are infrequent in reality and they restrict the number of times you can change your name.
How to Delete Google+
BEWARE (update 8/11/13): I just helped someone set up a Google account and then delete Google+. Because it had somehow linked her YouTube account with Google+, deleting Google+ deactivated her YouTube account and made her videos private. It was easy to fix, but could be confusing. Google is trying really hard to make people keep their Google+ accounts, whether they want to or not.