The United States does not keep a government register of private family arms. The American Heraldry Society puts it without ornament: citizens are legally free to assume arms of their own devising. There is no American king of arms, and no statute that makes a particular shield the property of a surname.
That is not the same as saying America has no heraldry. The same primer traces shields on colonial seals, on the arms of cities and colleges, and on the Great Seal adopted by Congress in 1782. George Washington’s personal arms are a matter of public record. Maryland still flies the Calvert arms. The habit crossed the Atlantic with the people who already used it.
Because the law is silent, the useful limits are ethical. The Society’s primer and its guidelines for practice treat another person’s arms as a mark of identity. To take them because the surname matches, without a proved line of descent, is the moral equivalent of wearing someone else’s name. Sharing a last name is not a grant.
Americans who want a new coat are asked, by those guidelines, to see whether the design is already in use, then to assume an original shield for themselves and their descendants. They may also petition a foreign office — the College of Arms, the Lord Lyon, and others — if they meet that office’s rules. A foreign grant does not become an American legal title. It is an honour and a record in that other country.
The oldest non-governmental heraldic body in the country is the Committee on Heraldry at American Ancestors, established in 1864 inside what was then the New England Historic Genealogical Society. The Committee says the United States has no statutory regulation of heraldry and no governmental authority charged with oversight. It keeps a Roll of Arms for immigrants and colonists whose shields were rightful in their country of origin before 1900. It also records modern assumed arms, and arms granted to Americans by foreign offices, as a scholarly register — not as a substitute for a Crown grant.
People looking for an “official” American office often find The Institute of Heraldry. It is a real office. It is not a family registry. It sits in the Department of the Army. Its public site describes decorations, flags, agency seals, organizational coats of arms, badges, and other official emblems. A Department of Defense feature on the Institute notes that the shop designs insignia for the armed forces and federal agencies, including presidential seals — not coats for private households.
Army regulation defines a coat of arms, in that federal setting, as a design on a shield used to identify units. That is organizational heraldry. It does not enroll your grandfather’s name.
For the English and Scottish rule that a surname does not carry a coat, see The crest is not the coat of arms. For the words on the shield itself, see How to read a coat of arms.