Achilles' name can be analyzed as a combination of ἄχος (akhos) "grief" and λαός (Laos) "a people, tribe, nation, etc." In other words, Achilles is an embodiment of the grief of the people, grief being a theme raised numerous times in the Iliad (frequently by Achilles). Achilles' role as the hero of grief forms an ironic juxtaposition with the conventional view of Achilles as the hero of kleos (glory, usually glory in war).
Laos has been construed by Gregory Nagy, following Leonard Palmer, to mean a corps of soldiers, a muster. With this derivation, the name would have a double meaning in the poem: When the hero is functioning rightly, his men bring grief to the enemy, but when wrongly, his men get the grief of war. The poem is in part about the misdirection of anger on the part of leadership.
The name Achilleus was a common and attested name among the Greeks soon after the 7th century BC.[1] It was also turned into the female form Ἀχιλλεία (Achilleía) attested in Attica in the 4th century BC (IG II² 1617) and, in the form Achillia, on a stele in Halicarnassus as the name of a female gladiator fighting an "Amazon". Roman gladiatorial games often referenced classical mythology, and this seems to reference Achilles' fight with Penthesilea but gives it an extra twist of Achilles being "played" by a woman.