From the Churches of Rome Wiki:
Santa Maria in Domnica is also known as Santa Maria alla Navicella and is dedicated to the Blessed Virgin Mary.
The church is believed to have originated in the 3rd or 4th century as a meeting-place for the first Christians of Rome and an institution for aiding the poor, in the home of the lady Cyriaca. The name is thought to reflect its origins, as 'domenica' is probably a corruption of 'dominicum', a common Latin word for 'church', and especially for house-churches. It was built on the site of a Roman barracks. Her family's cemetery was where the basilica San Lorenzo fuori le Mura stands, and it was Cyriaca who arranged the burial of St Lawrence, deacon and martyr. St Lawrence used to hand out alms to the poor here.
The present church is from the time of Pope Paschal I, who had it rebuilt 818-822. Many of the older elements were preserved, but side apses were added in the Eastern style.
Alterations were made by the titular priest of the church, Giovanni Cardinal de Medici, who later became Pope Leo X (1513-1521), with Andrea Sansovino as architect.
It got its alternate name Santa Maria alla Navicella after the small marble boat (navicella) in the piazza. The boat is a 16th century copy of an ancient one. The copy was placed here by Cardinal de Medici.
Among its titulars were Popes Stephen IX, Gregory VII, Clement VII, Tommaso and Giovanni Battista Orsini family, Innocenzo Cardinal Cybo, Federico Borromeo sen. (died 1589) and Tommaso Riario Sfroza.
At the present time, the titular priest of the church is H.E. William Joseph Levada.
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