You mean their parents didn't have nicknames for them while they were growing up?
There isn't a whole lot of family life in the book. The POV characters are exiles and hostages. The arena of conflict is mostly political and public. Whatever the tyrant Craterus' parents may have called him growing up, it's not going to be on the lips of the exiles plotting his overthrow. Some of the characters are athletes, who might presumably have nicknames, so that could be something to look at.