What is the name of the traditional Greek coffee served with grounds?

The traditional Greek coffee served with its grounds is called Greek coffee.

Greek coffee is prepared by simmering finely ground coffee with water, and optionally sugar, in a small pot called a briki. The coffee is poured unfiltered into a small cup, so the grounds settle at the bottom rather than being removed. It is normally sipped slowly, with the grounds left behind once the drink is finished.

This coffee belongs to the broader family of unfiltered coffee traditions found around the eastern Mediterranean and Balkans. Its preparation resembles Turkish coffee, and the two drinks are closely related in method. However, Greek coffee became the established national name in Greece, particularly after political and cultural tensions made the term Turkish coffee less acceptable in many Greek settings.

Greek coffee is not espresso: espresso is brewed under pressure and filtered into a concentrated shot. It is also different from frappé, a cold drink generally made by shaking instant coffee with water, sugar, ice, and sometimes milk. Frappe and freddo coffees are chilled beverages, whereas Greek coffee is traditionally served hot.