The son of Éomer Éadig, known as Elfwine the Fair. As the son of the King, he would most likely have held the rank of Marshal before he succeeded his father to become King of Rohan in the year IV 63. We know that both Meriadoc Brandybuck (known as 'Holdwine' in Rohan) and his friend Peregrin Took were present at the death of Éomer, so it seems reasonable to assume that they also witnessed Elfwine's coronation.
Notes
1
'Elf-friend' is also the meaning of the name Elendil, Aragorn's ancient and noble ancestor. In fact, Elfwine's name - in different forms and variations - has a long history in Tolkien's works. In some of his earliest writing (The Book of Lost Tales) we find a mariner named Ælfwine, and the name also appears in the story of The Lost Road, in various forms with the same root meaning (including Elwin and Alboin). Though all these characters were ultimately abandoned, their name survived to find its way into The Lord of the Rings, where it was given to the nineteenth King of Rohan. (The Book of Lost Tales comprises volumes I and II of The History of Middle-earth; The Lost Road appears in volume V of the same series.)