When I am using Ubuntu for commercial reasons, do I have to pay Canonical?

The trademark policy only applies if you wanted to the use the word "Ubuntu" in the name of your product - say you called your service "Ubuntu widgets".

However if you have your own name then you don't need to pay any money to Canonical (the holder of the Ubuntu trademark). You can use as much of the Ubuntu software and platform as you want without paying a penny, though you can pay for support.