The Rohirrim are citizens born in the realm of Rohan and they appear in The Lord of the Rings.
The name Rohirrim was mostly used by outsiders: the name they had for themselves was Eorlingas, after their king Eorl the Youngwho had first brought them to Rohan.
The terms Riders of Rohan and Riders of the Mark are commonly used and refer specifically to their mounted soldiers. The King's Riders were specifically the Riders who formed the bodyguard of the King.