Naomi married Ben Finney during his fourth year at Starfleet Academy. They moved into faculty quarters when he became a post-graduate instructor. The couple often socialized with James T. Kirk and his girlfriend Ruth. The night the Finneys announced Naomi’s pregnancy was the night Kirk and Ruth broke up.
Naomi gave birth to Jamie during Ben’s second year as a postgraduate instructor, either in 2252 or 2253. They remained in faculty quarters together for one more year, until Finney accepted his first post-graduate starship assignment aboard the USS Republic. (TOS novel: The Autobiography of James T. Kirk)