As far as I understand, I can use the name the same as the name of another business, if we are of different business natures. Right?
The other business is selling physical goods (more exactly, they are a peer-to-peer sales network). I sell files. Can I use their name for my business?
There is no intention on my part to use their name because it is their name. I first invented the name for my business, then with Google found there is already a business of this name.