Many of the characters in this play get their identities from their titles, which is why they obsess so much about their names. (This makes some sense given that members of the nobility are named after the land they inherit – like John of Gaunt, Duke of Lancaster.) The same is true of Richard II, who has inherited the title of King of England from his father. When Richard loses his title, he experiences a major identity crisis. Much like Shakespeare's character King Lear, Richard puts so much of his selfhood into his title that when he loses the crown, he finds it hard to define who he is. This is when Richard becomes the most interesting (and maybe even most sympathetic) figure in the play.
Bolingbroke's insistence that he be called "Lancaster" when he returns to England shows how powerful he thinks names are.
The fact that Richard experiences an identity crisis after being stripped of his title as king shows that he locates his power and his identity in his name and social role.