Rachel Cuddy is Lisa Cuddy's adopted daughter. She is the biological daughter of Natalie Soellner, the patient in Joy to the World and her boyfriend Simon. Natalie hid the pregnancy from her family and friends and when she went into labor, she panicked and fled to an abandoned house where she believed she had given birth to a stillborn baby and abandoned it.
Cuddy went to retrieve the body and was astounded to find that a homeless pair of squatters had found Rachel, revived her, and taken care of her. She convinced them to give her the baby to take back to the hospital.
None of the baby's grandparents felt they wanted to take care of her, so Rachel was placed in foster care. Cuddy volunteered to be the baby's foster mother.
Cuddy found that it was difficult to become attached to Rachel and considered giving her up. However, during a phone call with Gregory House and Allison Cameron over doing a dangerous procedure on another patient and Rachel crying, Cuddy found herself feeling more attached to the baby's needs. After that, she agreed to adopt Rachel.
Her mom Lisa Cuddy was dating and was engaged to Lucas Douglas through season 6. Lucas frequently babysat for Rachel - but since season the Season 6 episode Help Me, Cuddy has broken up with Lucas and is now dating Greg House. House babysat for Rachel in the Season 7 episode Unplanned Parenthood and she swallowed a coin when he left her unattended. He and James Wilson then spent the episode trying to keep Cuddy from finding out what had happened and waiting to see if the coin had passed through Rachel's system. Their efforts to escape detection failed. Cuddy found the dime while changing Rachel's diaper and, when she asked how Rachel came to eat a coin, Rachel blamed House.
Later, Cuddy became concerned about placing Rachel into a prestigious academy for preschoolers, largely due to the rigorous testing procedures performed on the children. Despite thinking the school was a bad idea, House secretly worked with Rachel in order to train her on the same toys, puzzles, & tests that the school would be using. Although there were ultimately no spots available for Rachel, despite her passing scores, the experience helped her and House to bond with each other.