When I lived in France I was always amused to hear this question in school, asking for my name for the first time, yet sounding as if people had already heard my name but forgotten it.
C'est quoi ton nom encore?
I think you could ask this question to be reminded someone's name, and this is especially indicated by the use of encore. But I must say that I remember being asked this question about my name more often when I met people for the first time.
My question is, how did this use of "encore" come to be? Has it lost its meaning of "once again" in this particular context, or does it emphasise any other connotation?