On the web: navigate to your Profile Page by clicking on your icon in the top-right corner of any Quora page, then clicking on your name in the drop-down menu.
On your Profile Page, mouse over your name and you'll see "Edit" appear to the right of your name. Click on "Edit", which will open a dialog box to change your name. After editing your name, click "Update."
On the mobile app: navigate to your Profile Page by tapping on your icon in the top-left corner, then tapping on your name in the drop-down menu.
On your Profile Page, tap on "Edit Profile", which is located just below your profile description. Update your name in the "Full Name" field. After editing your name, tap on "Save."