Paul Atreides is the owner of the company Arrakis, which designs, produces and sells perfumes. He creates a new perfume with a distinct aroma and a bright blue colour that he names ARRAKIS ATREIDES. The perfume is sold in a bottle shaped like the worms from which the perfume is extracted and is very expensive.

Alia Atreides is Paul's sister and she establishes a company also producing perfume but sold at affordable prices to the general public. She also produces a bright blue perfume packaged in the shape of a worm, but she calls it ALIA ATREIDES and it is sold at half the price of Paul's perfume.

Baron Harkonnen is Paul's aristocratic rival who makes every effort to undermine Arrakis. Two years after Paul commences sales of ARRAKIS ATREIDES, House of Harkonnen department stores start selling a blue perfume in snake shaped bottles called BARRAKIS BY BATREIDES.

Discuss the possibility of Paul Atreides registering any trademarks and any trademark infringement issues involving Alia Atreides and Baron Harkonnen.