Put anything related to any account in your password manager. Not only should your security questions have absolutely nothing to do with the real you, so should anything that’s not pertinent to the account. My first pet’s name or the name of my first car are often just random strings like my passwords and my names are randomly generated names.
Another route is to use the same fake info everywhere unless you need specific fake info which goes in the password manager.
If you’re not using a password manager you should start. Options like KeePass don’t require providers to have access to your info.