Catagories

I'll assume your question is about a Windows version of Quicken.

If that's correct you certainly can create your own Categories.  If you're entering a transaction in a register you can simply type in a new Category name as part of the entry process.  Quicken will ask if you want to create a new Category with that name and if you answer Yes, it will elicit some information about that Category. 

Alternatively you can click Tools > Category list > New Category and create a Category that way. 

Using a particular Category for a particular Payee doesn't mean that Payee must always use that Category.  If you have turned on "memorize payees" under Preferences then the next time you enter that Payee Quicken might very well suggest that Category, but you're free to change it for that transaction.