When the foreign princess converted to Russian Orthodoxy, prior to the wedding, they were given a new name, complete with patronymic. At that time, the princess was blessed under the Feodorovskaya Icon (Our Lady of St. Theodore), one of the most venerated icons owned by the Romanov family. Many of these princesses, including the last two Tsaritsas, took their patronymic from that icon.

I can't answer where the non-Feodorovna patronymics came from.