Ireyne has no official surname, having been an unrecognized bastard born in King's Landing. She was birthed from a Dornish woman, a former mistress of Aerys II Targaryen, who was sent to the Sept of Baelor to become a silent sister. Her child would start training to become a septa to give the king further atonement for his sins and ensure his heir wouldn't die.
She was born months before Viserys and raised primarily by her mother until the woman decided to leave her. From then on, the septas raised her and taught her the faith of The Seven. She had no contact with her father until after she began having dragon dreams at six-years-old. Soon after meeting Aerys, her dreams were deemed useless and faulty due to her impure lineage, but it was more likely that at her young age, she could not adequately describe them. While she was quickly dismissed and forgotten by him, the girl would forever be haunted by the disturbing image of The Scab King and the knowledge that he was her father.
When Viserys and his mother flee King’s Landing, Ireyne, is relocated with them only in hopes that her dragon dreams would be of future use as her father had become much more desperate by then. Both her and Dany are abused by their brother for years, with Ireyne enduring most of it to protect the younger girl. Though Viserys had always planned to marry Dany himself, when he has to betroth her to a Dothraki leader, he reluctantly shifts this burden to Ireyne instead.