That's not really any better. If a site is hacked that has your made up name, that gets published on the carder sites [1] along with your other information (email, credit card number, phone). It may not work to get a new credit card in your name, but it can be used to reset your password on some other crappy site that uses that information for "forgot password".
[1] https://krebsonsecurity.com/2017/12/the-market-for-stolen-ac...