The only truly correct options are חֲנֻכָּה or חֲנוּכָּה
However, holding that transliteration must exist, we can extrapolate the correct answers from the Hebrew.
Regarding the last two syllables:
- There is no dagesh chazaq in the nun, so there is no reason to double the "n" in the transliteration!
- There is a heh at the end, so there should be an "h" at the end.
- The kaf should not be translated as a double "k" or "c" because it has a dagesh qal, not a dagesh chazaq. While "k" is the most legible transliteration, q is welcome. Ck & C alone are not fully asur*, but are not recommended because they can lead to confusion in pronunciation and we should always build a fence around Torah.
The chet is a wildcard. Current acceptable options are ch, kh, x, ḥ, & 7, but I'm sure there's others floating out there. Using a regular "h" to transliterate a ח or כ is generally asur, so kal v'chomer** it's assur on a holiday that deals with Hellenism/assimilation.
This means the definitive list of current acceptable transliterations of the word "חֲנֻכָּה/חֲנוּכָּה" is as follows:
- chanukah
- chanuqah
- khanukah
- khanuqah
- xanukah
- xanuqah
- 7anukah
- 7anuqah
- chanookah
- chanooqah
- khanookah
- khanooqah
- xanookah
- xanooqah
- 7anookah
- 7anooqah
- ḥanukah
- ḥanuqah
- ḥanookah
- ḥanooqah
[Edit: follow-up post about lack of other dialects present in the list!]
* Asur / אָסוּר: (adj.) forbidden
**Kal v'chomer / קַל וָחֹמֶר: literally light and heavy; a halakhic phrase that essentially means "all the moreso"; an argument a fortiori for the legal & latin nerds