Game of Thrones: The Hand

A mysterious man becomes the Hand of the King. He serves under Aegon the Conqueror, following his every command. He appears when needed and kills when needed. He serves all who become King or Queen of Westeros. However, once Aegon dies, the Hand remains until he is replaced by another man, wearing exactly the same clothing as the man before him. Who are these mysterious men, or is it one man as each Hand of the King?