Henry and Clare name their daughter Alba, after a "white fortress on the hill." Her name mirrors her strength and assertiveness when Henry meets his daughter for the first time in the future at the Art Institute of Chicago. Alba is only ten years old, but Henry marvels at her maturity: "This the most self-possessed child I've ever met… where is Clare in this child?" Indeed it seems that Alba doesn't really resemble Clare. She has Henry's black curly hair and Henry's features. The proud father remarks, "She looks like me at ten." Then, of course, there's the most striking commonality: Alba is a time traveler as well.
Unlike Henry, though, Alba actually enjoys time travel. Although she, too, can't stop traveling, she has some measure of control over where and when she's going. She's even had some success with keeping herself in the present through singing. In general, she seems to readily accept the challenges of her strange life, one of which is that her father dies when she's only five.
Alba and Henry's distance in time and place doesn't seem to affect their emotional connection, though. When they meet at the Art Gallery, Henry is overwhelmed by Alba's love for and closeness toward him: "…this amazing child who presses against me as though she belongs to me…as though we have all the time in the world" (2.14.66). And they do. Henry makes a point of visiting Alba, allowing Alba to grow up with a father even though he passed away when she was five. They actually develop a normal father/daughter relationship – well, normal given the circumstances.
At the same time, Alba's condition forces her to grow up much quicker than normal children do. During one of her time travels to find Henry in the past, for example, she travels too far and sees Henry with his ex-girlfriend Ingrid, both of them drunk. While this might seem like a traumatizing experience for a young girl, Alba seems to handle the situation quite well. She even helps them find Ingrid's car. At the age of three, Alba also learns from an older version of herself that Henry will die when she's five. This revelation hits her hard, but she still has the strength to promise Henry to keep his death a secret from Clare. Kind of a lot to ask of a toddler, right? After that emotional blow to her young heart, several more follow: she has to witness Henry's depression over losing his feet, shortly followed by Clare's breakdown after Henry's death. It makes you wonder if time travel is the girl's only super power.