1. Go to Gravatar and sign in.
2. Delete your image.
3. Find your Gravatar profile, and click "Hide" at the bottom right.
4. Go to WordPress.com and sign in.
5. Click on the personal settings icon at upper right. (It looks like a head and shoulders in a circle.)
6. Go to the Security tab.
7. Under "Connected Applications," remove Gravatar.
For your WordPress.com account:
1. Sign in to WordPress.com.
2. Click on "My Site" at upper left and then on "WP Admin" to find the Dashboard for your blog.
3. In the Dashboard sidebar, click on Tools > Delete, and follow instructions.
4. Click on the personal settings icon at upper right.
5. Delete or change everything you want, including in your profile. (You can't delete the Public Display Name -- it will just come back -- but you can change it to "None" or something similar.)
6. Get a free throwaway address from a site like Mail.com.
7. Back at WordPress.com, go to the Account tab of your personal settings and change the email address to your new throwaway address. WordPress.com will send a verification email to that address.
8. Back at your throwaway email host, open the WordPress.com email and click the embedded link to verify the address. After that, you can delete the throwaway email account or leave it.
9. Back at WordPress.com, change the password to one that doesn't match any you use for other accounts. Optional: Make it a password you won't remember yourself.
10. Also optional: Under Account, change your username.
11. Sign out.