Daenerys Targaryen: Viserys! Please.
Moments later
Viserys Targaryen:
! Dany, tell them. (the gold melts) Make them! Make them... (he looks at drogo) No, you can't! (back at dany) Dany, please! (Drogo walks to Viserys with the pot)
Read more at: http://transcripts.foreverdreaming.org/viewtopic.php?f=67&t=7894
It makes sense for "Visy" the overbearing older brother to have a diminutive nickname for his little sister, who he's been a (not very good) father-like figure to while dragging her around Essos since she was a baby.
It doesn't make much sense for Dany who (at this point) was the frightened dependent younger sibling to have a diminutive nickname for the egotistical bully of an older brother she spent much of her life in fear of.
We know that Viserys took himself very seriously, calling himself a king and a 'dragon' in the face of constant mockery, and that he tended to take his frustrations out on his little sister who he threatened and bullied. In the TV show, all we really see of Dany's early years are her looking lost, depressed, fearful and passive in the first episode, and him casually threatening her in other episodes. In the books, we understand that she'd spent much of her early childhood dependent on Viserys, looking up to him in a Stockholm Syndrome sort of way, and she didn't begin to question his version of who he was until later.
The other nicknames Visy has (book only, if I remember right) are all mocking:
The few allies Visy had were people like Illyrio who massaged his ego in the hope of becoming the power behind the absolute ruler of a continent - they too would therefore not give him an irreverent, affectionate or childish nickname but would inflate his ego and encourage him to think of himself as a serious king.
Alias
| The Beggar King
| Khal Rhae Mhar (The Sorefoot King)
| Khal Rhaggat (The Cart King)
Other than that, none that we know of.
Dany only ever refers to him as "Viserys" or "her brother" in her POV chapters so it's likely that she never had a nickname for him. Which makes sense seeing as at the beginning of the story she is still afraid of him.
Viserys however, calls himself "The Dragon" on multiple occasions. Although this could be him referring to getting angry he calls it himself often enough it becomes a sort of nickname of himself.
"You will not fail me tonight. If you do, it will go hard for you. You don't want to wake the dragon, do you?" His fingers twisted her, the pinch cruelly hard through the rough fabric of her tunic. "Do you?" he repeated.
A Game of Thrones, Daenerys IHer brother had a simpler name. "Our land," he called it. The words were like a prayer with him. If he said them enough, the gods were sure to hear. "Ours by blood right, taken from us by treachery, but ours still, ours forever. You do not steal from the dragon, oh, no. The dragon remembers."
A Game of Thrones, Daenerys I
The people of the streets around Illyrio's palace and Pentos call him "The Beggar King".
Years past they had been forced to sell their last few treasures, and now even the coin they had gotten from Mother's crown had gone. In the alleys and wine sinks of Pentos, they called her brother "the beggar king." Dany did not want to know what they called her.
A Game of Thrones, Daenerys I
Lastly, the Dothraki call him "Khal Rhae Mhar" and "Khal Rhaggat", meaning "the Sorefoot King" and "the Cart King" respectively, though Viserys didn't know the meaning of the words taking them to be good things.
Dany followed on her silver, escorted by Ser Jorah Mormont and her brother Viserys, mounted once more. After the day in the grass when she had left him to walk back to the khalasar, the Dothraki had laughingly called him Khal Rhae Mhar, the Sorefoot King. Khal Drogo had offered him a place in a cart the next day, and Viserys had accepted. In his stubborn ignorance, he had not even known he was being mocked; the carts were for eunuchs, cripples, women giving birth, the very young and the very old. That won him yet another name: Khal Rhaggat, the Cart King. Her brother had thought it was the khal's way of apologizing for the wrong Dany had done him. She had begged Ser Jorah not to tell him the truth, lest he be shamed. The knight had replied that the king could well do with a bit of shame … yet he had done as she bid. It had taken much pleading, and all the pillow tricks Doreah had taught her, before Dany had been able to make Drogo relent and allow Viserys to rejoin them at the head of the column.
A Game of Thrones, Daenerys IV
