The flat top hat worn by Chassidish people (regular days)
This hat is called a "samet", and comes in "flach" (flat) or "hoicher" (higher) versions. There's also the open-crown Homburg style hat that's common in Chassidish circles.
The bent hat worn by Lubavitcher Chassidim
This is simply known as a fedora as in English or a "bent-down hat". The pinches in the crown are known as "knaitches" (pinches). They're usually manufactured by Borsalino, it's the classic fedora.
The hat worn by contemporary Litvish people
This is the same hat that's worn by Lubavitch Chassidim, just it generally has a wider brim and a taller crown. I've usually just heard this called a fedora like in the above example or "the black hat".
Source: my own experience.