The queen is married to Richard. Technically and historically she has a name (Isabella), but Shakespeare never mentions it in this play. (Technically and historically she was also a child of about ten when Henry took the crown from her husband, but Shakespeare makes her an adult.) In fact, in the "dramatis personae" (the list of characters), Shakespeare lists her under "King Richard II" and refers to her as "The Queen, his wife." What's that all about?
We've got a few ideas, Shmoopsters. Think about it: the queen's role in this play is pretty much limited to the domestic world (as opposed to the political world), which means that her main function in the play is to be a wife – nothing more and nothing less.
In fact, the queen is totally clueless when it comes to political matters. This is especially clear when she says goodbye to Richard as he's being led away to prison. Check out this passage, where she begs Northumberland to banish Richard to France with her instead of locking him up, so they can be together:
Banish us both and send the king with me.
That were some love but little policy. (5.2.4)
As Northumberland points out, it wouldn't be very smart for King Henry to send Richard to France with his wife. He could come back with an army and challenge Henry. Or worse, he could father a child with his wife, and the kid could grow up and decide to make a legal claim to the crown. But the poor queen just doesn't get it, which is pretty heartbreaking if you ask us. Shakespeare's not making fun of the queen for being ignorant of politics; he's showing us an incredibly sad and loving moment between a wife and her husband.
At the same time, the queen is also pretty intuitive. In Act 2, Scene 2, she has some kind of psychic premonition about all the troubles Richard is going to face. She says, "methinks / Some unborn sorrow, ripe in fortune's womb, / Is coming towards me" (2.2.1). In a way, the queen is an interesting foil for Richard: what he fails to see until the crown is practically taken away from him, she guesses at from a distance.