What are the names of the two blue wizards?

Question

What are the names of two blue wizards? Gandalf said (in The Hobbit movie) that there were five wizards and that he forgot the name of the blue wizards.

Answer 1

Elsewhere in the canon (in "Unfinished Tales") their names are given as "Pallando" and "Alatar". Those names are used in many derivative works, eg the collectible card game.

Much later in his life he wrote more about the blue wizards and named them Morinehtar and Rómestámo ("Darkness-slayer" and "East-helper"). Since Gandalf (and Saruman) had alternative names this is not necessarily a contradiction.

This is discussed in detail at the Tolkien Gateway article.

Answer 2

The Blue Wizards had several different names depending on which unpublished writing you look at.

Undated - Alatar and Pallando

Of major interest, however, is a brief and very hasty sketch of a narrative, telling of a council of the Valar, summoned it seems by Manwë ("and maybe he called upon Eru for counsel?"), at which it was resolved to send out three emissaries to Middle-earth. "Who would go ? For they must be mighty, peers of Sauron, but must forgo might, and clothe themselves in flesh so as to treat on equality and win the trust of Elves and Men. But this would imperil them, dimming their wisdom and knowledge, and confusing them with fears, cares, and weariness coming from the flesh." But two only came forward: Curumo, who was chosen by Aulë, and Alatar, who was sent by Oromë. Then Manwë asked, where was Olórin ? And Olórin, who was clad in grey, and having just entered from a journey had seated himself at the edge of the council, asked what Manwë would have of him. Manwë replied that he wished Olórin to go as the third messenger to Middle-earth (and it is remarked in parentheses that "Olórin was a lover of the Eldar that remained," apparently to explain Manwë's choice). But Olórin declared that he was too weak for such a task, and that he feared Sauron. Then Manwë said that that was all the more reason why he should go, and that he commanded Olórin (illegible words follow that seems to contain word "third"). But at that Varda looked up and said: "Not as the third;" and Curumo remembered it.
The note ends with the statement that Curumo [Saruman] took Aiwendil [Radagast] because Yavanna begged him, and that Alatar took Pallando as a friend.
_{Unfinished Tales - "The Istari"}

1959 - Palacendo and Haimenar

2175. Oromë remains for 12 years, and then is summoned to return for the councils and war-preparations. Manwë has decided that the Quendi should come to Valinor, but on urgent advice of Varda, they are only to be invited, and are to be given free choice. The Valar send five Guardians (great spirits of the Maiar) with Melian (the only woman, but the chief) these make six. The others were Tarindor (later Saruman), Olórin (Gandalf), Hrávandil (Radagast), Palacendo, and Haimenar. Tulkas goes back. Oromë remains in Cuiviénen for 3 more years:VY 866/13-16, FA 2175-8.
_{The Nature of Middle-earth - "Key Dates"}

1972 - Morinehtar and Romestamo

The 'other two' came much earlier, at the same time probably as Glorfindel, when matters became very dangerous in the Second Age. Glorfindel was sent to aid Elrond and was (though not yet said) pre-eminent in the war in Eriador. But the other two Istari were sent for a different purpose. Morinehtar and Romestamo. Darkness-slayer and East-helper. Their task was to circumvent Sauron: to bring help to the few tribes of Men that had rebelled from Melkor-worship, to stir up rebellion ... and after his first fall to search out his hiding (in which they failed) and to cause [?dissension and disarray] among the dark East ...
_{The Peoples of Middle-earth - "Last Writings"}