I found the "Valar color alignment theory" intriguing, so I decided to do some research (it helps to have a PDF version of the professor's works). Unfortunately, the Silmarillion does not corroborate and even contradicts this theory.
For example, the color grey is not associated with Manwe or Varda anywhere in the Canon, but with other Valar such as Nienna:
And Nienna arose and went up onto Ezellohar, and cast back her grey hood, and with her tears washed away the defilements of Ungoliant;
Estë the gentle, healer of hurts and of weariness, is his [Irmo] spouse. Grey is her raiment; and rest is her gift.
As for the color white, the only passages where this color is mentioned in association with the Valar is:
At times he [Ulmo] will come unseen to the shores of Middle-earth, or pass far inland up firths of the sea, and there make music upon his
great horns, the Ulumuri, that are wrought of white shell;
He [Orome] is a hunter of monsters and fell beasts, and he delights in horses and in hounds; and all trees he loves, for which reason he
is called Aldaron, and by the Sindar Tauron, the Lord of Forests.
Nahar is the name of his horse, white in the sun, and shining silver
Telperion [created by Yavanna] was the elder of the trees and came first to full stature and to bloom; and that first hour in which he
shone, the white glimmer of a silver dawn, the Valar reckoned not into
the tale of hours, but named it the Opening Hour, and counted from it
the ages of their reign in Valinor. (also by Yavanna: Nimloth, the
White Tree of Númenor)
A reference to white that has "conflicting interests" as it refers to snow (of which Iluvatar himself said it was the joining of the works of Ulmo and Aule):
Taniquetil the Elves name that holy mountain, and Oiolossë Everlasting Whiteness, and Elerrina Crowned with Stars, and many names
As for the color blue, there are references to Manwe and Varda, but not to Orome:
His raiment is blue, and blue is the fire of his eyes, and his sceptre is of sapphire, which the Noldor wrought for him;
It is told that even as Varda ended her labours, and they were long, when first Menelmacar strode up the sky and the blue fire of Helluin
flickered in the mists above the borders of the world, in that hour
the Children of the Earth awoke, the Firstborn of Ilúvatar
There are no references to brown in the Silmarillion.
The only color association that the Silmarillion somewhat validates is therefore Gandalf by his association with Nienna - it is stated she wore a grey hood. Given that Gandalf was her student, this might have some relevance to his title.
So I did some further digging, and found another possible relation - the etymology of the color names in Quenya and Sindarin:
White: from the root *glân, (S and Q) originally meaning pure. However, I don't believe the word pure implies Saruman (who's original name Curunir translates as cunning) but to the White Council he preceded. The White Council was formed to challenge Dol Guldur, the lair (dol) of the Necromancer (guldur), literally "perverted or evil knowledge". It therefore stands to reason that the name White Council was chosen not for the color, but the implied purity of knowledge protected by that council.
Grey: *mith(S), Gandalf was called Mithrandir, Grey Pilgrim, by the Eldar.
Blue: The Blue Wizards Pallando and Alatar are called the Ithryn Luin because it is said they arrived in Middle-earth by boat dressed in sea-blue (luin). However, luin stems from lhun, which also means boat.
Brown: no translation for Radagast is provided by Tolkien. However, a possible root for the name may be the Old English rudugást, meaning brown spirit.