Hi,
Let's just say that the group of your name is "Internet Cafe" and just for the sake of this example, we'll just say 인터넷 카페 in Hangeul even though that's actually English.
So if you wanted to say, "hello, I am Internet Cafe's Angie." or "hello, I'm Angie from [the] Internet Cafe" -- I would say "안녕하세요, 저는 인터넷 카페의 앤지라고 합니다."
*Pronunciation tip: When you say 의, just keep in mind that it's pronounced more like 에 when spoken.