The mark has more to do with making an intelligent choice than with a physical mark. God has a method of identifying those that are His. God also has a method for identifying those that belong to Satan.
If one decides to take the mark, then a physical identifier of some type most likely will be used. A control system such as a microchip, nanobots, transponders, smart card, tattoo, or other tech devices may be implemented. The control system identifies those who can buy and sell in the marketplace and the like. Not all is yet understood regarding this matter. However, as faithful Christians, the time will be made obvious when the Mark arrives in its fullness.