Não só Elrond usa "Gandalf" em vez de "Mithrandir". Galadriel também o chama de 'Gandalf':
"Gandalf the Grey set out with the Company, but he did not pass the borders of this land." (LotR II 7 - The Mirror of Galadriel)
E Celeborn faz o mesmo na mesma cena:
"If it were possible, one would say that at the last Gandalf fell from wisdom into folly" (ibid)
Os elfos de Lothlórien usam 'Mithrandir' quando cantam em sindarin:
Often they heard nearby Elvish voices singing, and knew that they were making songs of lamentation for his fall, for they caught his name among the sweet sad words that they could not understand. Mithrandir, Mithrandir sang the elves (ibid)
Esta evidência apoiaria a ideia de que, como @Janus diz no comentário, os Elfos usaram 'Mithrandir' quando falaram em Sindarin, e 'Gandalf' quando usaram o Westron.
Legolas aborda Gandalf como 'Mithrandir duas vezes, aparentemente quando ele deveria ter usado' Gandalf '(se a hipótese acima estiver correta), mas ambos são exclamações de surpresa, quando alguém pode entrar no modo mais acostumado do que o que poderia ser considerado "mais adequado". Primeiro, quando eles acreditam que Gandalf morreu e eles mesmos são seguidos por Saruman:The old man was too quick for him. He sprang to his feet and leaped to the top of a large rock. There he stood, grown suddenly tall, towering above them. His hood and his grey rags were flung away. His white garments shone. He lifted his staff, and Gimli's axe leaped from his grasp and fell ringing on the ground. The sword of Aragorn, stiff in his motionless hand, blazed with a sudden fire. Legolas gave a great shout and shot an arrow high into the air: it vanished in a flash of flame.
'Mithrandir!' he cried. 'Mithrandir!'
'Well met, I say to you again, Legolas!' said the old man. (LotR III 5 - The White Rider)
Na mesma conversa, um pouco mais tarde, quando ele está mais calmo, ele usa 'Gandalf':
"It would ease my heart, Gandalf, to hear what befell you in Moria." (ibid)
E mais uma vez, quando Gandalf vem para quebrar o cerco em Helm's Deep:
'Behold the White Rider!' cried Aragorn. 'Gandalf is come again!'
'Mithrandir, Mithrandir!' said Legolas. 'This is wizardry indeed!' (LotR III 7 - Helm's Deep)