The piazza still bears this name, which is derived from the extinct Branca family.

After the death of her former husband she must, therefore, have moved from the house on the Piazza Pizzo di Merlo and taken up her abode in the one on the Piazza Branca.

This house may have belonged to her, for her second husband seems to have been a man without means, who hoped to make his fortune by his marriage and with the protection of the powerful cardinal.
From a letter of Ludovico Gonzaga, dated February 19, 1488, we learn that this new marriage of Vannozza's was not childless.

In this epistle, the Bishop of Mantua asks his agent in Rome to act as godfather in his stead, Carlo Canale having chosen him for this honor.

The letter gives no further particulars, but it can mean nothing else.[11] We do not know at just what time Lucretia, in accordance with the cardinal's provision, left her mother's house and passed under the protection of a woman who exercised great influence upon him and upon the entire Borgia family.
This woman was Adriana, of the house of Mila, a daughter of Don Pedro, who was a nephew of Calixtus III, and first cousin of Rodrigo.