The name bronies gave her is a word that has been used on the Internet for a long time, however it's meant to mock disabled people (esp. people with Down syndrome). Not like such behavior is anything new for certain sections of the 'net but the MLP staff wasn't aware and when the writer of the episode she first spoke in found out what that word means, she was appalled (apparently her son is autistic) and removed it competely.
I really don't like it when people call her that word. But I call her Bubbles personally!
Some others I've seen are Bubblecup, Muffin/Muffins, Miss Muffin and the (muffin emoji) pony.