Why Pallas? As far as I know, this figure is not particularly common (among ancient Greek mythological figures) to have as a bust, and "The Raven" is such a well-crafted poem that surely every word is carefully chosen. Is it just for the alliteration in the phrase "pallid bust of Pallas", or is there some deeper significance in the choice of this particular figure?
Poe himself offers a brief answer to this in his 1846 essay The Philosophy of Composition. He states:
I made the bird alight on the bust of Pallas, also for the effect of contrast between the marble and the plumage—it being understood that the bust was absolutely suggested by the bird—the bust of Pallas being chosen, first, as most in keeping with the scholarship of the lover, and secondly, for the sonorousness of the word, Pallas, itself.
This offers up a minor conundrum: there are a number of figures in Greek mythology named Pallas, but none of them is particularly associated with scholarship. From this we can deduce that Pallas in the poem refers to the common epithet of Athena, goddess of wisdom.
Why use Pallas rather than the more common name, or Homer's frequent choice of "Pallas Athena"? Because Poe felt it was "sonorous". The poem is in trochaic octameter, a rare meter of eight metric feet (each "foot" is a stressed and unstressed syllable) per line. Athena is three syllables, whereas Pallas is two, so we can imagine the choice to essentially be:
Perched upon a bust of Pallas just above my chamber door—
Perched upon a bust of Athena above my chamber door—
The two syllable choice fits the overall rhythm of the poem better (it has very few three syllable words), punctuates that rhythm better with the hard "p" beginning the foot rather than the softer "a", avoids the direct alliteration of "Athena above" which might sound odd to read aloud in favour of the more pleasing broken alliteration of "perched" and "Pallas" and, finally, as Poe says, contains that sonorous "s".
We learn early on that the protagonist is educated and has a thirst for learning:
Once upon a midnight dreary, while I pondered, weak and weary,
Over many a quaint and curious volume of forgotten lore
And this is why he is likely to have a bust of Athena in his chamber, to represent the wisdom and knowledge that he seeks. By extension, we can also imagine that Athena represents the logic and rationality that comes from learning.
The titular raven, by contrast, represents the protagonist's grief over his lost love, Lenore. Ravens are often associated with death, as is the black colour of its plumage. Having flown in and perched upon this symbol, the raven then does a most un-ravenlike thing. It speaks:
Quoth the Raven “Nevermore.”
And this is further evidence of the raven's symbolism of grief, since "nevermore" is also the answer to the protagonist's desire to see his lost love once again:
Tell this soul with sorrow laden if, within the distant Aidenn,
It shall clasp a sainted maiden whom the angels name Lenore—
Clasp a rare and radiant maiden whom the angels name Lenore.”
Quoth the Raven “Nevermore.”
However, the raven also has a second symbolism in the poem: irrationality. We can see this in the way it speaks, since no rational mind would believe a raven was capable of speech nor engage it in dialogue as the protagonist does. We see it also in the nature of this dialogue as he attempts to impose some sort of reason upon the situation, providing repeated questions to the raven to which the answer might conceivably be "nevermore", yet the raven cannot respond in any kind of rational way. The speaker also imbues the bird with supernatural symbolism:
“Prophet!” said I, “thing of evil!—prophet still, if bird or devil!—
Which is, of course, the very opposite of logic and rationality. Given the way the speaker keeps returning to the subject of Lenore, it's not hard to imagine that his grief over his lost love is beginning to unhinge his mind, resulting in his half-hearted conversation with a bird.
The reason for choosing Pallas is thus to highlight this contrast. The bust is white and represents rationality and immortality. The raven is black and represents irrationality and mortality. By the raven choosing to roost upon the bust and, meaningfully, never leaving, we can see that it represents the way that grief disorders reason. Indeed since the raven is still sitting on the bust at the end of the poem, it seems that the protagonist may never fully recover from their grief, nor the scholarly acumen they seem to prize.