예, 맞습니다. Yes, it is right, but it is a formal and generous expression for older people than you. If you meet people at your age or younger, then you can say "안녕, 나는 Eunice야" or "안녕, 난 Eunice야". However, I recommend you say "안녕하세요, 저는 Eunice입니다." even to young people, if you meet him/her for the first time.