Dr. Paul Whitehead, who heads the forensic unit at Utah State Hospital, was discussing Brian David Mitchell's delusions, the Deseret News reported.
Mitchell and his wife, Wanda Barzee, allegedly kidnapped Smart, then 14, from her home in Salt Lake City in 2002 and held her for nine months as a second wife. Mitchell is charged with kidnapping and sexual assault.
Whitehead said Mitchell wanted Smart to have a child and suggested to her that she could rejoin her parents in a decade, introducing them to a grandchild.
"Mitchell was talking to Miss Smart about having babies to the point that Smart actually picked out a name if that happened," Whitehead said.
Smart quickly left the courtroom, followed by her mother. Her father walked out briefly earlier in Whitehead's testimony.
Mitchell's lawyers argue that he is mentally ill. Whitehead is one of a series of witnesses to talk about his mental condition.