The name migrated into Swedish as 'Pitronella', which was her baptismal name. When she came to the US as a girl of 11, she shortened it to 'Nelly', a common name at the time, and an equally common shortening of Pitronella. She used it the rest of her life and her tombstone bears it.She always worried that it wasn't her 'real' name, but in those free and easy days before identity theft and 9/11, in most jurisdictions, you could use any name you liked, as long as there was no fraud or criminality involved.
Rest in peace, Grandma!
Here is a bit about St Petronilla from Catholic Online:
St. Petronilla is believed to have been the daughter of St. Peter. Until the XVII Century, she was called his physical daughter, and since then, she has been thought a spiritual daughter who was consecrated to his service. Legends quoted in Manichćan documents relate that Peter cured her of a palsy. Stories found in the writings of St. Marcellus (and retold in The Golden Legend) say that Peter, who thought his daughter too beautiful, asked God to afflict her with a fever, of which he refused to cure her until she began to be perfected in the love of God. She is said to have refused Count Flaccus' hand in marriage. Traditions say she died a natural death, but accounts of her martyrdom can be found. Petronilla is thought to have been Aurelia Petronilla, a scion of the gens Flavius, the family of Vespasian and Domitian. She was also related to St. Domitilla, who was exiled in I Century to Pandateria, whose property on the Via Ardentina became a catacomb cemetery. Inscriptions there describe Petronilla as a martyr. During the papacy of Siricius (384-399), a basilica was built on the site of her tomb. In the VIII Century, Gregory III established a place of public prayer in the basilica, and her relics were translated to St. Peter's, where a chapel was dedicated in her honour. Charlemagne (d. 814) and Carloman (d. 771) were considered adopted sons of St. Peter, and they, along with the French monarchs who succeeded them, considered Petronilla their sister.