The word Hannukah is derived from the verb khanakh, which means to consecrate or dedicate.
The kabbalistic symbolism of Hannukah, as I have understood it from a lecture by Rav Michael Laitman, is as follows. Hannukah symbolizes the passing over the barrier between receptivity (passivity) and giving (activity). This corresponds to the individual’s experience of something outside of or beyond themselves, and their consequent acquisition of new vessels of the soul. The oil of the candle symbolizes our individual substance. The wick symbolizes the masakh, a word literally meaning sheet, curtain, or veil. The masakh is our individual resilience and will to defend ourselves. The fire is the light of God, which burns away the masakh and the individual, consuming them in Divine Truth. Hannukah represents the successful rectification of the first two layers of the soul; after Hannukah, there are three more layers to purify through the same process of burning them away and reacquiring them in the form of pure vessels. The pre-Hannukah self-conquests are a war with the Greeks, and the post-Hannukah self-conquests are a war with the Romans. The final perfection of the individual is symbolized in Purim, a celebration of the saving of the Jews from a holocaust.
The lecture I derived this from is titled “Kabbalah for the Nation: What is the meaning of Hanukkah?”