A person who has a coat of arms is sometime called an armiger. They are armigerous.
Originally an armiger was an Armour-Bearer or Esquire, who helped a Knight, but who had his own coat of arms.
The term "armiger" is well-defined only in countries such as the United Kingdom, Canada, Ireland, and Spain where there is a state or other heraldic body. These bodies include the College of Arms in England, Wales, and Northern Ireland, the Office of the Chief Herald in the Republic of Ireland or the Court of the Lord Lyon in Scotland).
Someone can have a coat of arms either because they are descended from a person with a right to bear a coat of arms, or by having a new grant of arms to him or herself.
Armiger Facts for Kids. Kiddle Encyclopedia.