Nós já sabíamos que seu nome verdadeiro não era Hodor, mas Walder (livros) e Wylis (programa de TV). Aprendemos a origem de "Hodor" no 5º episódio da 6ª temporada.
SPOILERS FOR S06E05:
We see that when Meera, Hodor and Bran are trying to exit the cave in order to escape the Night King and his army, Meera is carrying Bran on the sledge and tells Hodor to "Hold the Door" over and over, in order to prevent the White Walkers from exiting the cave and catching up to them.
While this is happening, Bran is viewing the past and inadvertently warged into Wylis (Hodor's real name), thus linking the present day Hodor with young Wylis. Hodor then has a fit and falls to the ground, while shouting "Hold the door" repeatedly. He gradually removes some words (Hold the door -> Hold door -> Hodor) and that is how he started saying Hodor.
Scene link.
Há também um "Inside the Episode":
Onde David Benioff diz que esta é na verdade a mesma origem para o nome como nos livros.