Letters introducing oneself is called 자기 소개서 (introductory letter), which sometimes shortened to 자소서. Such letters are generally in free form, so you can use whatever way you think best conveys the contents. As for not writing things like '안녕하세요, 제 이름은 ... 입니다', it is true, and the reason is because such vital information is usually separated out in bullet forms in the beginning of the letter. It's generally not a good idea to give such information buried deep in a paragraph. Here's one sample letter format. You can also search for 자기 소개서 (sometimes shortened to 자소서) on the website of the school you're applying to or on the internet at large. ([] mark translated parts, not part of the content.) ........................................................자기 소개서 * 작성일: 2016년 11월 10일 * 인적 사항 [Applicant's personal information]: Marie S ... 20세. 여. [name, age, sex] * 연락처: (전화 번호)......[telephone number] ................(이메일 주소)..[email address] ................(주소)..............[mailing address] * 지원 학사 과정 [name of the degree program or courses you're applying for]: ... ( some space here ) 1. 지원 동기 및 포부 [Reasons for applying and future plans] ... (paragraphs) 2. 성장 과정 및 교육 [Upbringing and educational history] ... (paragraphs) 3. 성격 [Personality] ... (paragraphs) 4. 취미 및 기타 사항 [Hobbies and other facts] ... (paragraphs)

you can write your name in case of just letter for friendship. but you have to write recommendation letter and i can't guarantee. i can help you for Korean but i don't know about that. i think there is a form of recommendation letter definitely. so you'd better find the form and other people's letter who is already exchange student. how about search internet cafe or blog for exchange student or contact professor or administration office first?