Hello, you can look here on how to recover a Facebook account.
However, as you have created an account with a 'fake name', then you won't be able to verify your Identity. Although possible, technically Facebook doesn't allow people to create fake name accounts. Hence why FB will ask for proof of ID for the fake name account, which you won't be able to give.
If you have been logged out because you are using a VPN / there has been suspicious activity on your account, FB should allow you to verify your account using the email or mobile no. that you used to set up the account.
If you remember all your account's credentials then you can easily sign-in to your account. But if you don't remember then your can use "Forgot Password" and then follow the facebook steps to regain access.