Notoriety ends random street brawls with the Blighters: they no longer start conflicts with you. It costs only money, no materials.
Notoriety is entry 2 of 9 in the Insider branch, one of the three branches (Ringleader, Insider and Swindler) on the Rooks' 39-upgrade board. It is bought with money and materials, not skill points: £7,500. Before Notoriety unlocks you need Police Bribes.