The more the emergency medical team knows about your health history, the better. The name and phone number of your primary care doctor, in addition to any specialists you've seen or are seeing, is important information to bring to the ER. In fact, it's a good idea to carry that information with you at all times, right along with your medical history.
Additionally, emergency workers and hospital personnel want every single one of us to carry in case of emergency (ICE) information, either tucked in a wallet or as an entry to a phone contacts list. ICE information should include, at the very least, the name and contact numbers for the person or people who should be called by the paramedics, police or ER staff if you're in an accident or have any other type of emergency. Make sure the person listed as your emergency contact knows that they'll be contacted if there's an emergency, and review your medical history and regular doctor's information with them.