how did it get it's name?
Tolkien used Old English for the kingdom's language and names.
Rohan (Middle-earth)
Tolkien used Old English for the kingdom's language and names, 
where is rohan in lord of the rings It is bordered to the north by the Fangorn forest, to the northeast are the walls of Emyn Mui, to the east are the mouths of the River Entwash, and the Mering Stream, to the south lie the White Mountains and to the west are the rivers Adorn and Isen.
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Rohan (Middle-earth) [SEP] Introduction
Rohan is a kingdom of horsemen, the Rohirrim, in J. R. R. Tolkien's fantasy setting of Middle-earth. It is mainly a grassland, and provides its ally Gondor with cavalry. Rohan is grounded in Anglo-Saxon tradition, poetry, and linguistics, in everything but its use of horses. Tolkien used Old English for the kingdom's language and names, pretending that this was in translation of Rohirric. Meduseld, King Théoden's hall, is modelled on Heorot, the great hall in "Beowulf". In "The Lord of the Rings", Rohan is important in the action, first against the wizard Saruman in the Battle of the Hornburg, and then in the climactic Battle of the Pelennor Fields.