The dining hall where Leonardo painted The Last Supper is called a refectory.
A refectory is the communal dining room of a monastery or convent. Leonardo’s mural occupies the end wall of the Dominican convent of Santa Maria delle Grazie in Milan, placing the biblical meal in the same kind of room where monks would gather for their own meals.
The setting was practical as well as symbolic. Religious communities commonly decorated refectories with scenes of the Last Supper, encouraging diners to associate their shared meal with Christ’s final meal with his disciples. The opposite wall of the room contains a Crucifixion painted by Giovanni Donato da Montorfano.
A refectory is not the same as a cloister, which is a covered walkway around an open courtyard. Nor is it a chapel: the mural is in the convent’s dining hall. Leonardo’s painting was commissioned during renovations connected with Ludovico Sforza’s plans for the complex.