Does Kakashi, or Iruka tell others about their relationship first?
I think that Kakashi would tell his friends first willingly, and Iruka’s friends would coax the first confession out of him.
It’s not that Iruka is ashamed to be with Kakashi, he just gets embarrassed easily, and knows what Konoha’s gossip ring is like, so he wants to keep their relationship theirs for as long as possible (because once word gets out that they’re dating, people would be watching them all the time, and probably ask him a bunch of questions that he doesn’t want to answer).
But since he can be particularly hot-headed, if his friends tease and badger him enough about out, he will snap and tell them in a burst of anger… Which might have been how they found out he liked Kakashi in the first place 
Kakashi, on the other hand, secretly likes all the attention; and because he is in love with Iruka and everything about him, he wants to show him off to the world. “Look at this sexy man! He’s mine!”, he wants to say.
But in the beginning, he only tells Gai & Tenzou, the only people he trusts not to tell anyone, while he waits (im)patiently for the news to slip or for Iruka to share the news around, himself… And the guys can’t wait for that to happen, because Kakashi just doesn’t stop talking about him! 
What do you think?