How to introduce yourself

Do you know how to introduce yourself in Arabic when you meet someone for the first time?
When someone asks you

اسمك يه؟
Ismak(for a man) ismek (for a woman) eih, which means "What's your name?" you answer:

اسمي... 
Ismi...  
My name is... +your name

Sometimes after hearing your name people say a strange phrase

عاشت الأسامي
3ashat el-asami
(3 stands for ع)  Which literally means "Names live", and not literally "Long live the name", "Let your name be remembered after you die" or just to make it simple let's say it means "Nice name".

So now you want to say "nice to meet you" so you say :

فرصة سعيدة
Fursa sa3eeda

And the answer will be:

أنا أسعد
Ana as3ad