Fedora

A fedora /fɨˈdɔərə/ is a felt hat.
The word fedora comes from the title of an 1882 play by dramatist Victorien Sardou, Fédora, written for Sarah Bernhardt

The hat is typically creased lengthwise down the crown and "pinched" in the front on both sides. Fedoras can also be creased with teardrop crowns, diamond crowns, center dents, and others, and the positioning of pinches can vary. The typical crown height is 4.5 inches (11 cm).
The brim is usually approximately 2.5 inches (6.4 cm) wide, but may be wider, can be left "raw edged" (left as cut), finished with a sewn overwelt or underwelt, or bound with a trim-ribbon.
Fedoras can be found in nearly any colour, but black, grey, tan, and dark brown are the most popular
[Wikipedia]

And as we all know a man isn't properly dressed without a hat and a cane.