Is it permissible to name a daughter after her deceased sister, and is it true that naming two siblings with the same name will result in them being nameless on the Day of Resurrection?

There is no objection to naming more than one son or daughter with the same name, whether the first is alive or deceased. This practice was found among many of the righteous predecessors, such as the repetition of the names Muhammad, Ja'far, Zaynab, and Umm Kulthum among the children of Ali ibn Abi Talib, may Allah be pleased with him. The Companion Ka'b ibn Malik al-Ansari had two sons, both named Muhammad. Therefore, it is incorrect to claim that naming two brothers with the same name will cause one of them to be lost on the Day of Resurrection.