A trench coat and fedora are supposed to make you inconspicuous (E.g. Incognito tabs, detectives) by if you ever went out in public in that, you'd be the most conspicuous person there. :
The Vintage Trench Coat | a little bit of rest
Bogart's Trench Coat and Suit in Casablanca » BAMF Style
The Vintage Trench Coat | a little bit of rest
In Favor of the Double-Breasted Trench Coat - Tailor & Barber