The name of Lady Ma’sumah, is Fatimah. In historical books and hadith sources, her eminence is referred to as Fatimah bint Musa ibn Ja’far. She wasn’t technically an infallible, the way the prophets and imams were, although she was at a very high level of spiritual purity and perfection. It is noteworthy to say that infallibility is something relative. Considering the hadiths about her rank and status, it can be said that she possessed a degree of infallibility – not at the level of the imams of course.
Lady Ma’sumah’s actual name is Fatimah. In historical books and hadith sources, her eminence is referred to as Fatimah bint Musa ibn Ja’far, although it has been hundreds of years that she is known by the title ‘Ma’sumah’, to the extent that nowadays for Iranians, this title has turned into her real name.
Lady Ma’sumah wasn’t an infallible in the sense that the imams and prophets were, however, she possessed a high degree of spiritual purity and perfection, to the extent that paradise has been promised to the zuwwar (visitors) of her grave.
It is noteworthy to mention that infallibility is a relative concept, and considering the hadiths on the rank and status of Lady Ma’sumah, it can be said that she possessed a degree of infallibility, albeit not that of the imams. Such a claim isn't deemed unlikely for a personality like her, the reason being that what is meant by such infallibility is being free from sin and never sinning, which is something that even some great scholars were able to achieve.
Shaykh Saduq, Uyun Akhbar al-Rida (AS), vol. 2, p. 267, Jahan Press, Tehran, first edition, 1378 (solar).
 See: Majlisi, Bihar al-Anwar, vol. 106, p. 168.
 An infallible is one who, through God’s grace, refrains from all forms of sin and ugly and inappropriate acts; this being out of free will and not force, and while having the ability to commit them. Also, an infallible is one who is free of all forms of error and mistake. His excellence, Imam Ja’far Sadiq (AS) says in this regard: “المعصوم؛ هو الممتنع بالله من جمیع المحارم. و قد قال الله تبارک و تعالی: و من یعتصم بالله فقد هدی الی صراط مستقیم” (The ma’sum [infallible] is one who by Allah, is protected from all sin and Allah has said “And whoever takes recourse in Allah is certainly guided to a straight path”, Shaykh Saduq, Ma’aani al-Akhbar, p. 132, Jame’eye Modarresin Press, Qum 1361 (solar), adopted from the question: The concept of infallibility and the possibility of the infallibility of individuals, 249.
 Amili, Shaykh Hurr, Wasa’il al-Shia, vol. 14, p. 576, hadith 94, Aal al-Bayt Institute, Qum, 1409 AH, “
مُحَمَّدُ بْنُ عَلِيِّ بْنِ الْحُسَيْنِ فِي ثَوَابِ الْأَعْمَالِ وَ عُيُونِ الْأَخْبَارِ عَنْ أَبِيهِ وَ مُحَمَّدِ بْنِ مُوسَى بْنِ الْمُتَوَكِّلِ عَنْ عَلِيِّ بْنِ إِبْرَاهِيمَ عَنْ أَبِيهِ عَنْ سَعْدِ بْنِ سَعْدٍ قَالَ سَأَلْتُ أَبَا الْحَسَنِ الرِّضَا (ع) عَنْ زِيَارَةِ فَاطِمَةَ بِنْتِ مُوسَى بْنِ جَعْفَرٍ (ع) بِقُمَّ فَقَالَ مَنْ زَارَهَا فَلَهُ الْجَنَّة”.
 See: Hurr Amili, Wasa’il al-Shia, vol. 14, p. 576, hadith s 19850 and 19851.