There is also the theory that the nickname "Sisi" was from her father. He visited egypt and was very interested in this country and its history. When you read "Sisi" from the end to the beginning you got "Isis", the important egypt godess. But well thats only another theorie...
Sophie was really called "Sopherl" but only in when she was a child, she didn't like these nickname, so everyone called her Sophie or the most closest friends and familymebers called her by her second name Charlotte. It was a privileg to call her so and her husband Ferdinand got it after their first "romantic hours" at saxony.