You can use Shopify's free fraud filter app if you just want to block an existing customer. You can just add their email address to block them from making a new order from an existing account.
If you need more advanced blocking features and options like preventing the same customer from creating a new account, then you might want to look into more advance app like Beacon.
I hope this helps.
The solution suggested by @Jason_Beacon is really the first thing we would recommend, so please do look into the Fraud Filter app and test it out for this customer.
Another app option for blocking or restricting customers is the Locksmith App.
This app allows you to block users based on many different conditions, including by blocking an IP address. The app has a 15 day free trial so you can look into it and try it out before you commit to any subscription payments.
I also wanted to ask - how did you determine that the orders generated were fake? Any further context you can provide here would be helpful, and I will see if there is anything else we can suggest for you.
Let me know if you have any other questions.