It is also known as الرقية the incantation in a hadith mentioned in Bukhari وَمَا يُدْرِيْكَ أَنَّهَا رُقْيَة how did you know it was an incantation? Other names include الحمد al-Hamd since it starts with the حمد praise and thanks of Allah. It is also known as الكافية the sufficient, because of its importance in prayer. If a person recited surah Al-Fatihah in his prayer and did not recite any other surah in the Quran it would be enough to meet the minimum requirements for prayer, but if someone did not recite surah Al-Fatihah and recited the rest of the entire Quran his prayer would be invalid.
Other less well known names are الشفاء the cure because of a hadith in which states فاتحة الكتاب شفاء من كل داء the opening of the book is a cure from every disease, though this hadith is ضعيف weak, الكنز the treasure, الواقية the preventer and الأساس the foundation.