Is there a connection between naming a baby girl after her sister who died in an accident and her recurrent illnesses?

Belief in Divine Decree (Qadar (definition)), both its good and bad, is a fundamental pillar of faith. The Messenger of Allah (peace and blessings be upon him) said in the Hadith (definition) of Jibreel: "To believe in Allah, His angels, His books, His messengers, and in Divine Decree, both its good and its bad." Quranic verses and prophetic traditions confirm that everything is created by decree, and that Allah's command is predetermined and effective. The name of the deceased has no effect on the health and life of the newborn, for everything that befalls a person, be it health, sickness, poverty, or wealth, is by Allah's preordainment and decree, regardless of the name. The majority of people bear the names of their deceased fathers and mothers, or the names of prophets and righteous individuals. If the name of a deceased person had an effect on the one named after them, most people would be sick or dead. One must believe that all occurrences are by Allah's preordainment and decree, for whoever believes in this will face trials with a firm heart and a tranquil soul.