Homeric Hymn 28: to Athena starts out with one of the most beautiful descriptions of Athena I have ever read and encompasses many of Her fine qualities, including Her wisdom, Her ideals, and Her birth from the head of Zeus. In that regard, the writer made use of the epithet and title 'Tritogeneia':

"I begin to sing of Pallas Athena, the glorious goddess, bright-eyed, inventive, unbending of heart, pure virgin, saviour of cities, courageous, Tritogeneia. From his awful head wise Zeus himself bare her arrayed in warlike arms of flashing gold, and awe seized all the gods as they gazed."
 
Tritogenia, here, is clearly intended to refer to the word 'tritô', signifying 'head'. The word is found in the ancient Cretan, Aeolic, and/or Boeotian language and would lead to a meaning of 'the Goddess born from the head' for the full title. That said, this cult title--unique to Athena--has had various interpretations over the years, and  would like to collect them here today.

Besides a grammarian interpretation, there are also those ancient writes who link 'Tritogeneia' back to Athena's birth place at Lake Tritonis in Libya, or the river Triton near Alalcomenae in Boeotia. This interpretation is found in Apollodorus' 'Bibliotheca', and in Euripides' 'Ion':

"Zeus had intercourse with Metis, who turned into many shapes in order to avoid his embraces. When she was with child, Zeus, taking time by the forelock, swallowed her, because Earth said that, after giving birth to the maiden who was then in her womb, Metis would bear a son who should be the lord of heaven. From fear of that Zeus swallowed her. And when the time came for the birth to take place, Prometheus or, as others say, Hephaestus, smote the head of Zeus with an axe, and Athena, fully armed, leaped up from the top of his head at the river Triton." [Apollodorus, 1.3.6]

"But, by the starry throne of Zeus, and by the goddess high above my rocks, by the sacred headland of Triton's watery lake, I will no longer conceal this bed, so that I may cast off this load from my breast and be at ease." [Euripides, 870]

Athena also had a cult following near the river Triton, so the name may have been derived from the Goddess worshipped there. It is my personal view, though, that the Goddess worshipped at the river Triton is most often referred to as 'Pallas Athena', where Pallas does not so much (although partly) derive from her spear-wielding capabilities, but from Her childhood friend Pallas, whom Athena accidentally killed during mock combat. This is noted down by Apollodorus in his 'Bibliotheca', abide another section than before:

"The story told about the Palladium is as follows: They say that when Athena was born she was brought up by Triton, who had a daughter Pallas; and that both girls practised the arts of war, but that once on a time they fell out; and when Pallas was about to strike a blow, Zeus in fear interposed the aegis, and Pallas, being startled, looked up, and so fell wounded by Athena. And being exceedingly grieved for her, Athena made a wooden image in her likeness, and wrapped the aegis, which she had feared, about the breast of it, and set it up beside Zeus and honored it. But afterwards Electra, at the time of her violation, took refuge at the image, and Zeus threw the Palladium along with Ate into the Ilian country; and Ilus built a temple for it, and honored it. Such is the legend of the Palladium." [3.12.3] 

Some say that this Athena was a daughter of Poseidon and Tritonis, the nymph of the lake Tritonis; Pausanias in his 'Description of Greece' is a good example:

"Above the Cerameicus and the portico called the King's Portico is a temple of Hephaestus. I was not surprised that by it stands a statue of Athena, be cause I knew the story about Erichthonius. But when I saw that the statue of Athena had blue eyes I found out that the legend about them is Libyan. For the Libyans have a saying that the Goddess is the daughter of Poseidon and Lake Tritonis, and for this reason has blue eyes like Poseidon." [1.14.6]

To me, it is entirely possible that 'Tritongeneia' refers to this epithet of Athena as well. There are a few variations of the epithet, namely 'Trito', 'Tritonis', 'Tritonia', and 'Tritogenês', which all allude to different interpretations, but nearly all of them seem to trace back to Libya in some way or another, and all relate to Her birth--abide different versions of it. Tritogeneia is an interesting title, and unique to Athena. Its origins might be a bit vague, but it is a respectable title none the less.