What's up with the title? You know the answer to this. There's a king named Richard II... but he won't be a king for long. That's why the publishers of the first quarto edition of the play (printed in 1597) called it The Tragedy of Richard II. The tragedy being that Richard gets knocked off the English throne and tossed in the slammer where he has an emotional meltdown right before he's murdered. (Psst. You can check out the original title page here.)
What's interesting is that, later, when the first folio edition of the play (printed in 1623) came out, it was called The Life and Death of King Richard the Second. (Check out the title page here.)
What does this title change tell us? Well, the folio publishers probably thought of the work as more of a history play than a tragedy. We talk about all this tragedy vs. history stuff in "Genre," so go there if you want to know more.