I know it doesn't make much of a difference, as Gmail forwards all messages to "john.doe" and "johndoe" to the same inbox, but I don't want it there anymore. The
. shows up whenever my Gmail username is displayed across Google products.
According to Google, it is not possible:
You can't change the email address on your account to an existing Gmail address, but we invite you to add a new Gmail address to your Google Account.