Santissimo Nome di Maria al Foro Traiano is one of the two familiar domed landmark churches at the north end of the Imperial Fora, just by Trajan's Column . It is the larger one (the other is Santa Maria di Loreto), and is dedicated to the Holy Name of Mary. The postal address is Foro Traiano 89. Pictures of the church on Wikimedia Commons. 
The first church on this site was San Bernardo a Colonna Traiani, which had been taken over by the Confraternita di San Bernard''o in 1440(the church is first recorded in 1418). This was a secular confraternity devoted to charitable works, originally founded at the Cistercian abbey of Tre Fontane and using the church of Santi Vincenzo e Anastasio alle Tre Fontane located there. This little church was also dedicated to Our Lady, and had on its high altar an ancient icon of the Blessed Virgin which had once been in the chapel of San Lorenzo in Laterano. This had been given to the confraternity by Pope Eugene IV in about 1430, when it was still based at Tre Fontane, and was believed to have been painted by St Luke. The side altars were dedicated to St Bernard of Clairvaux and St Nicholas, and the ceiling had a fresco of St Bernard in Glory by Avanzino Nucci. The dedication to St Nicholas came from another little church, San Nicolò della Colonna, which was actually attached to Trajan's Column and was pulled down as a result in an early fit of antiquarian puritanism in 1541. The confraternity remained here until 1585, when they moved to Santa Susanna. They were then responsible for setting up the Cistercian nunnery there. The church of San Bernardo became nothing more than a devotional chapel, attracting pilgrims wishing to venerate the icon.
The feast of the Holy Name of Mary was introduced by Blessed Pope Innocent XI (1676-1689) victory over the Ottoman Turks at the second Siege of Vienna in 1683. This battle permanently broke the power of the Turks in Europe. A cult of the name was instituted in San Stefano del Cacco in 1685 by Dom Giuseppe Bianchi, an abbot from Sabina of the Sylvestrine monastic congregation (now Benedictine). Soon after, he established a Confraternity of the Most Holy Name of Mary (Confraternita del Santissimo Nome di Maria) which was formally approved in 1688 in order the propagate the devotion. In 1694, they moved to San Bernardo, which was in a bad state of repair by then, and renovated the building. However, they decided that the church was too small, so they acquired the adjacent plot and built the present church from 1736 to 1741. The architect was French, Antoine Dérizet. The older church was only demolished in 1748.
The actual site they acquired was the north-eastern corner of the small Piazza di Colonna Trajana, so that the new church was only attached to other buildings for a quarter of its circumference. The famous column was in the opposite, south-western corner of the piazza. Opposite the church were the back doors of the monasteries of Sant'Eufemia and Santo Spirito ai Monti. These were demolished for archaeological excavations even before the French occupation, in order to uncover the Basilica Ulpia of the Forum of Trajan. Thus the present, anomalous situation of the church was created, whereby it looks over a vast excavation containing ancient Roman bits. The Second World War arguably saved the church, and much else, from demolition since Fascist "archaeologists" suspected (probably incorrectly) that the undiscovered Temple of Trajan lies underneath.
Like Dérizet's other church in Rome, Santi Andrea e Claudio dei Borgognoni, this is a dome with a church tucked underneath. The ground-plan is based on a square with the front corners chamfered. Superimposed on this is the dome itself, which has a very tall drum and is just slightly elliptical.
The exterior walls are all in white. The first storey has pairs of Composite pilasters occupying its corners, and supporting an entablature. Two pairs of semi-round Composite columns flank the entrance, and above the entablature corresponding to these is a blank segmental pediment with its central section recessed. The rest of the entablature is crowned by a balustrade which supports free-standing statues of saints.
The drum of the dome has eight pairs of double Corinthian pilasters, and in between these are eight large round-headed (not arched) windows with curved raised lintels above looking rather like eyebrows. The dome itself, in lead and with eight large ribs corresponding with the paired pilasters, has eight round windows in Baroque frames with volutes. The intricately designed lantern has eight little swagged Ionic columns with tall arched windows in between and eight flaming torch finials above. There is an ogee cupola supporting a central ball finial.
The interior is slightly elliptical, corresponding with the dome so that there are no pendentives. There are six small chapels, richly decorated in polychrome marble and separated by gigantic Corinthian pilastes in veined pink marble with gilded capitals. These chapels contain good paintings of the mid 18th century. Above the chapels on the diagonals are galleries with balustrades. The interior of the dome is decorated with white and gold stucco work, with garlands and palm fronds and eight medallions with reliefs. A symbol of the Trinity is in the oculus. Four lapis lazuli plaques bearing titles of Our Lady are on the entablature below.
The side chapels are (left to right): SS Peter and Paul, with an altarpiece by Lorenzo Masucci of 1750; St Bernard, with an altarpiece by Niccolo Ricciolini of 1751; the Crucifix; St Joseph, with an altarpiece showing the death of the saint by Stefano Pazzi as well as stucco work by Andrea Bergondi; St Anne, with an altarpiece showing her teaching Our Lady to read by Agostino Masucci of 1751, as well as a sculpture of Our Lady from the previous church; and finally St Aloysius Gonzaga, with an altarpiece by Antonio Nesi of 1740.
The main altar has as its altarpiece the ancient icon of Our Lady, enshrined in a spectacular Baroque gloria. Note the pair of bronze double-headed eagles on the flanking pilasters, emblems of the Hapsburg Empire whose capital Vienna was.
Once a year, the icon is taken in solemn procession from the site of the now destroyed church of San Bernardo to its present place in this church.