On Athena's epithet 'Pallas'

"Hello, can you help me maybe? :) I haven't been able to find out what Athena's epithet "Pallas" means?"

'Pallas' is one of those epithets of which the origins have pretty much been lost. In Hómēros this name always appears united with the name Athena, as Pallas Athênê or Pallas Athênaiê. In later writers we also find Pallas alone instead of Athena. The most probable explanation is that 'Pallas' is the same word as 'pallax', i.e. a virgin or maiden, but there are many more options.

Plato in 'Cratylus' derives the surname from pallein, to brandish, in reference to the goddess brandishing the spear or aegis:

"Hermogenes: Still there remains Athene, whom you, Socrates, as an Athenian, will surely not forget; there are also Hephaestus and Ares.
Socrates: I am not likely to forget them.
Hermogenes: No, indeed.
Socrates: There is no difficulty in explaining the other appellation of Athene.
Hermogenes: What other appellation?
Socrates: We call her Pallas.
Hermogenes: To be sure.
Socrates: And we cannot be wrong in supposing that this is derived from armed dances. For the elevation of oneself or anything else above the earth, or by the use of the hands, we call shaking (pallein), or dancing.
Hermogenes: That is quite true.
Socrates: Then that is the explanation of the name Pallas?
Hermogenes: Yes; but what do you say of the other name?
Socrates: Athene?
Hermogenes: Yes.
Socrates: That is a graver matter, and there, my friend, the modern interpreters of Homer may, I think, assist in explaining the view of the ancients. For most of these in their explanations of the poet, assert that he meant by Athene "mind" (nous) and "intelligence" (dianoia), and the maker of names appears to have had a singular notion about her; and indeed calls her by a still higher title, "divine intelligence" (Thou noesis), as though he would say: This is she who has the mind of God (Theonoa);- using a as a dialectical variety e, and taking away i and s. Perhaps, however, the name Theonoe may mean "she who knows divine things" (Theia noousa) better than others. Nor shall we be far wrong in supposing that the author of it wished to identify this Goddess with moral intelligence (en ethei noesin), and therefore gave her the name ethonoe; which, however, either he or his successors have altered into what they thought a nicer form, and called her Athene."

Pseudo-Apollodorus has two explanations. The first is that it is a honourable mention to the giant Pallas, who was slain by Athena. Then there is his explanation in 'Bibliotheca', where he links the name to Athena's youth and her friend Pallas:

"They say that after Athene's birth, she was reared by Triton, who had a daughter named Pallas. Both girls cultivated the military life, which once led them into contentious dispute. As Pallas was about to give Athene a whack, Zeus skittishly held out the aegis, so that she glanced up to protect herself, and thus was wounded by Athene and fell. Extremely saddened by what had happened to Pallas, Athene fashioned a wooden likeness of her, and round its breast tied the aegis which had frightened her, and set the statue beside Zeus and paid it honour." [3.144]

Athena would have taken Pallas' name as a way to honour Her and keep Her memory alive, as it was an ancient Hellenic belief that the dead whose name was spoken remained tied to the person and family.

Which (if any) of these the true origin is, I do not know. Personally, I follow the latter explanation due to UPG reasons. Which one works for you is--naturally--up to you.