Translation:She has not yet told me her special name.
I put "She has still not told me her special name", but marked wrong. My feeling as a native UK English speaker is that both English sentences mean exactly the same - the "not yet done smth" is a bit posh sounding/bookish - not something you would normally hear in everyday speech. However, I acknowledge that if you change the word order, that does sound more usual - She has not told me her name yet".
Adding "yet", whether within or concluding the sentence, gives additional information that the speaker is expecting to be told in the future, it just hasn't happened YET. Without that, the implication is that it hasn't happened and there isn't necessarily an expectation that things will change.