Nam made her first South Korean team, as a 15-year-old, at the 2000 Summer Olympics in Sydney, where she competed in the women's 200 m individual medley.

Swimming in heat two, she raced to fourth place and twenty-seventh overall by nearly five seconds behind winner Hana Černá of the Czech Republic in 2:22.53.

[4] At the 2004 Summer Olympics in Athens, Nam placed seventh in the 400 m individual medley with a time of 4:50.35, edging out Greece's Vasiliki Angelopoulou by exactly half a second (0.50).

She eclipsed a FINA B-standard entry time of 4:52.38 from the Dong-A Swimming Championships in Ulsan.

[7] In the 400 m individual medley, she topped the first heat by five seconds ahead of Singapore's Quah Ting Wen with a time of 4:46.74.