The synagogue service that includes the Rosh Hashanah Amidah with Malchuyot, Zichronot, and Shofarot is Musaf.
Musaf is an additional prayer service recited on Shabbat, festivals, Rosh Chodesh, and other special occasions. On Rosh Hashanah, its Amidah is distinctive: instead of the usual central blessing found in many weekday prayers, it contains three major sections devoted to kingship, remembrance, and the shofar.
These sections are called Malchuyot, Zichronot, and Shofarot. Each traditionally includes biblical verses connected with its theme. The Amidah therefore has nine blessings in total: the standard three opening blessings, three closing blessings, and the three Rosh Hashanah-centered middle blessings.
Musaf is often confused with Shacharit because both are part of the morning synagogue schedule. Shacharit is the regular morning service, while Musaf follows it as an additional service. The shofar may be heard before Musaf and, in many communities, during the repetition of the Musaf Amidah. Practices vary by rite and by whether Rosh Hashanah falls on Shabbat.