Fedora, Trilby Hat

Similar hats with a C-crown (with an indentation for the head in the top of the crown) are occasionally called fedoras. The brim goes all the way around, and often there will be a hat band as well. A trilby hat is somewhat similar to a fedora, but typically has a shorter brim, and the back of the brim is distinctively more sharply upturned as a result.

Source: Wikipedia > Fedora