Coupled with your profile picture, your Blogger display name identifies you not just on your own blog, but also in the comments you leave on other people's posts. If the display name you chose when you signed up no longer suits you, you can change it by editing your Blogger profile, provided your blog isn't linked to your Google+ profile.
Editing the Profile
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To change your display name, click on your name in the upper-right corner of the Blogger dashboard and select "Blogger Profile" from the drop-down menu. This opens your Blogger profile. To edit it, click the "Edit Profile" button. Replace the name in the text field labeled "Display Name" with the new display name you want to use, scroll to the bottom of the page and click "Save Profile." Blogger returns you to the "Edit User Profile" screen, with a confirmation at the top that your changes have been saved. Your display name can be a maximum of 200 characters long and each Blogger account can have only one display name. If you need different names for different blogs, create the blogs using separate accounts.
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If You're Using Google+
If you're blogging with a Google+ profile, you won't see a display name on the Blogger dashboard, since the name under which your posts and comments appear is tied to your Google+ account. If that's the case, the only way to change your display name is to disconnect Blogger from your Google+ account. To do this, click the gear button at the top of the page, select "Revert to Blogger Profile" and then click "Switch to a Limited Blogger Profile." Enter your desired display name in the text field and then click "Continue to Blogger" to return to the dashboard with a confirmation message at the top.