It might matter what you call the company or the product, however, since that is the brand that the people who pay you are seeing.
Programmers are so literal. Let me try and translate: When Patrick says "don't call yourself a programmer" he isn't necessarily saying "never use the word 'programmer' in the same sentence as your own name". What he's saying is: When someone asks you what you do all day, don't just say "I program... stuff" or "I program in Lisp". What do you program? Why? What value do you create thereby?