1. 16th century ~ 1990s: 林 - 임 2. From 1990s: In 1990s, the rules of orthography for Chinese names changed. For the people who are before the modern age, we still avoid ㄹ as an onset of a syllable. 李 and 林(리and 림 in Korean pronunciation system), therefore, are still 이 and 임 when they are at the onset of a syllable. For the people who are of the modern age, we recognize and accept / l, r / in their names. Some examples: 1) o o 林 王健林(Wáng Jiànlín) : 왕젠린 * 중국 기업가(1954- ). 완다(萬達, Wàndá) 그룹 창립자·회장. 2) 林 o o 林語堂(Lín Yǔtáng) : 린위탕 * 중국의 작가·문명 비평가(1895 -1976). The name of this Chinese writer had been 임어당 until it changed into 린위탕 in 1990s in Korea. From the official website for the Korean Language; http://www.korean.go.kr/front/foreignSpell/foreignSpellList.do?mn_id=96&pageIndex=1

Since its your name, you can choose however you want but recognize that Koreans might not have an L sound like you are used to hearing.