I'm not sure this is what you wanted to know, so if it isn't, then just tell me. =P
Negi owns these special pills that can make you older or younger, depending on it's color. red makes you older, and blue makes you younger. It gets noticed alot that Negi's older form talks, looks, and acts like Negi, so he started to go as "Nagi" while older, off of his father's name.
he also recieved these special pieces of paper from one of his students, Setsuna, that can create clones or tiny floating versions of the user that can talk to the user and the user only through telepathy, hence the "Chibi-Nagi".