Can someone enlighten me on this?

So my FWB wants me to call him daddy or sir, but typically refers to himself as daddy. He is a dominant. I have read up on this, would that make him a Daddy Dom? He calls me a good girl when he likes something I do and if I do something he dislikes I will get punished. He wants me to refer to him as those two names all the time even if we're out in public together and around our friends but he is still really affectionate, like kissing me and holding my hand and loving on me. Does this sound correct? It's all still a little new so I don't know. If someone has any experience I this area and could enlighten me on some things to expect or do to make this an easier transition into that would be great:) Thank you!