What is the organization that makes a do board-certified?

ACOM. American college of osteopathic medicine.
Board exams. The american college of osteopathic physicians does certify dos. Dos can also take specialty certification exams for allopathic physicians (mds) such as the american board of internal medicine (abim), american board of pediatrics (abp), etc.
Depends. Depends on the board for which they are eligible after completing training. If they did a do residency, then they must seek board certification through the aoa and its constituent boards, such as the american osteopathic board of surgery. If they completed an md residency then they must seek board certification through the american board of medical specialties and one of its 24 constituents.