Ever since the establishment of the first colonies in America, the Puritans continued to enforce the same Bastardy Laws as they existed in England as of the 1660's. Hawthorne was spot on in describing the manner in which aldermen expected women who became pregnant out of wedlock to openly declare the father of the child, since the pain that comes out of childbirth should not be bare alone.
According to Puritan law, a child who is born out of wedlock is considered, like with Pearl, an "elfin" or something supernatural that will never make it to heaven due to the sins of the mother.
A strange child!” remarked old Roger Chillingworth. “It is easy to see the mother's part in her. Would it be beyond a philosopher's research, think ye, gentlemen, to analyse that child's nature, and, from it make and mould, to give a shrewd guess at the father?As a result, some women would rather confess to fornication than follow the humiliating consequences of bastardy laws.
Hence, since the children were not recognized by a specific family, the most likely answer is that Pearl carried Hester's last name of "Prynne". This is ironic considering that Hester's last name is that of her husband, Roger.
However, last names for the likes of Pearl were really not necessary. The girl was not to be baptized, presented, nor allowed in church-related activities. She was to suffer the same isolation as her mother. More than likely, Pearl was not even accounted for in the population because, as a result of her mother, she would not be considered as a worthy community member. Therefore, although her last name does not really matter (nor does it come up in the novel), the likelihood of it being her mother's own last name is quite high.