To disable your entire profile, click on "Disable my account" in your settings: https://www.duolingo.com/settings/account.
Please be careful as this will disable all your Duolingo-related accounts!
Your account will be fully deactivated, but you will be able to re-activate it yourself by logging in again. If you deactivate your account, your username and email associated with your account will be reserved so that nobody else can sign up with those. Any messages in the forum posted by you under this account will appear as [deactivated user] unless you re-activate the account.
Be advised that if you are a Duolingo Plus subscriber via the mobile apps, disabling your account will not suspend charges, as those are done by Apple or Google. Please refer to this article if you need to adjust your Plus payment settings on Apple and Google.
If someone used your email address to sign up for Duolingo without your consent, please read "Someone created a Duolingo account with my email. How can I remove it and unsubscribe?"
If you are looking to completely delete all your information and account, please read How can I delete my account and data? (your username will not be reserved for you if you choose this option).