First name, last name, and NPI is all you should need.
Medicare also maintains a list of NPI's by name. If a provider is not in the list, that provider cannot refer services for Medicare patients, but since this is for an HMO the list is not exhaustive:
http://www.cms.gov/Medicare/Provider-Enrollment-and-Certification/MedicareProviderSupEnroll/MedicareOrderingandReferring.htmlClick the "Medicare Ordering and Referring File - CSV [ZIP, 9MB]" to download the files, there are so many names that CMS put the first half of the alphabet by last name in the first file, and the other half in the second. It's fantastic to have to deal with. Also, there are a lot of duplicate names, which is frustrating, so you may have to call the provider to verify you have the correct NPI.
To find an NPI, hit Ctrl+F and enter the last name of the person you're looking for.
Edited post to remove some info, it's looking like some of the issues we're having with this new requirement are not with Medicare.