Looking around for subway info - I learned that they are simply a licensed trademark of Doctor's Associates Inc. Strange company name, huh? Could be useful in slightly deceiving the public during marketing campaigns - though I can't remember any instances.. It's tough to do these days (with the internet, blogs, etc) - but you have to think that they had some fun in the 80s..:) Also, they really bury "doctors associates inc" - rather, they refer to themselves as "the SUBWAY chain" often. I like their reason behind the franchisor title:

6. Who are the doctors in Doctor’s Associates Inc (DAI)?

When the company was founded, Dr. Peter Buck, co-founder, was a scientist with a doctoral degree, and Fred DeLuca had aspirations of becoming a medical doctor. Hence the name Doctor’s Associates.
link here

Aspirations of becoming a medical doctor - Nice!