I have a student named 선미 (Seon-mi). Her name reminds me of the character Sonmi in Cloud Atlas (novel by David Mitchell, movie written and directed by Lana Wachowski, Tom Tykwer and Lilly Wachowski – trailer, spoilerific final sequence (subtitled in Turkish, of all things!)), but the names aren’t necessarily the same.
Korean ㅓ approximates to the English ‘short o’ (as in John) and ㅗ to ‘long o’ (as in Joan). There is no indication as to how the book/movie character’s name is spelled in Korean: the book doesn’t include any hangeul (and very few Korean words) and the movie has hangeul only on buildings and vehicles in the background. (Korean Wikipedia’s page on the movie doesn’t transliterate the names of the characters.) The difference in pronunciation is sometimes small or non-existent: a ㅗ followed by a syllable-final consonant sounds very much like ㅓ – a suburb is a 동 (dong), which is always pronounced with a short o.
Romanisation of Korean needs to distinguish between the two letters. Yale uses e (inexplicably) and o, McCune–Reischauer ŏ and o, and Revised Romanization eo and o, so in any system, Sonmi is more likely to be 손미.
Many people informally use u or ou for ㅓ (and 삼성 (RR = sam-seong) and 현대 (RR = hyeon-dae) officially use u and the related yu), but the three major systems all use u for ㅜ and none uses ou at all. Many people use oo for ㅜ. Cloud Atlas actress 배두나 (bae du-na) spells her name ‘Doona’, which is just the wrong image for me. At least it’s a darn sight better than the MR transliteration of Pae Tu-na.
[Update: I have two students in the same class named 희선. One uses the spelling Hee-seon, the other Hee-sun.]