Excuse me, what does Dabai mean?

I'm guessing it's his Name

It's the nickname of YuYang's roommate/friend.
It's also the Chinese name for Baymax (the big white robot from the Disney animation). Characters for Dabai （大白）mean "big + white"。

So Cappy he is talking to a roommate on the phone not his handsome friend that we saw more recently when LiHuan brought YuYang back from the bar?

That handsome friend is HuanWen and i think he's the one Yy refer to as dabai

The handsome friend you are talking about is Chu HuanWen, the design department's President of the student council.

Dabai is one of YuYang's roommates, the dark grey and yellow shirt guy in this picture: http://iweb7.mangapicgallery.com/r/newpiclink/here_u_are/27/67337c34bdf55388b5716d7e117487cf.jpeg

Confusing, huh? 90% of the characters have their hairs in some shade of grey...
(⊙…⊙ )

And then she draws them in chibi style so ... I guess I don't know who it is

yeah whops DJun is he - forgot again!

I keep forgeting it, too!
but he seems to not care about that.
at least in his Twitter account, people refer to him as a "she" and he doesn't bat an eye about that.