Bunny is Oscar's sister. She appears in a Season 41 episode of Sesame Street as a surprise guest for Grouch Mother's Day. Oscar's mother gave her the name Bunny just to annoy her. In April 2011, Oscar answered a couple questions about his sister in the following interview:
Was your mother also a grouch?
Oh yes, I come from a long line of grouches. I have a sister, her name is Bunny. Mom named her that just to tick her off. She’d rather have had a name like Geezelah or Grumpy, because she is, trust me, a grump.
Do you see her often?
Hopefully not, although it is kind of fun when she comes because we argue the whole time. Grouches like a good argument. I’m only worried about this because I haven’t been disagreeable enough. I guess I got out of the right side of the bed. You’re too pleasant. ... And I love being miserable. That makes me happy. But I don’t like being happy, so that makes me miserable. I’m a mess. I’m a complex grouch.