noun
trilby
TRIL-bee/ˈtrɪlbi/
A soft felt hat with a narrow brim and an indented crown.
The felt trilby has a narrow brim and a pinched, indented crown.

Etymology
The hat takes its name from the fictional heroine Trilby O’Ferrall. Her character wore this type of soft felt hat in the stage adaptation of the novel.
In context
suddenly there's a loud bang and a bullet goes straight through murphy's trilby taking it off his head and sending it flying into the road