How do you pronounce "Hacan" in Twilight Imperium?
Short answer: Ha- Kahn



Rationale:

There is no official pronunciation from Fantasy Flight as of yet (and I hope they don't release one, because this is one of the best things to argue about in the game).  That said, we have some theoretical basis to come up with one by considering that "proper" pronunciation will vary by language.

The first question we have to ask is whose word is "Hacan"?  Is that their spelling or the Anglicization?  I am assuming here that the language of Federation of Sol descends from English, which is not a perfect assumption since Sol is both the English and the Latin name for the sun, but they do at least use the latin alphabet.  I would further assume that "Hacan" is the Anglicization or at least "Solanization", since it is written in the latin alphabet.  A lion race probably has different phonemes than humans (due to their different anatomy and vocal chords) and the true pronunciation may not be easily expressed in the Latin alphabet.

The true pronunciation in Hacaneese is probably something with a growl or a roar in the middle, since this is a race of lions, and I assume that is what is implied by the heavy use of A's in the word.  Similarly, I assume that the Xxcha begins with a clicking of the beak that can only be properly made with a beak (that humans lack).

This then leaves us with the question of how close "Hacan" is to the actual word in Hacaneese.  There are three typical possibilities.  One is that it is very close.  For example, the typical English pronunciation of "Shanghai" is only off by one phoneme from the proper pronunciation in Mandarin (ignoring tones).  Another is that it is an approximation with some creative liberties, such as the English "Belgrade", which bears only mild resemblance to the Serbian "Beograd".  Finally, we could be in a situation where we use a totally different word, such as "Germany" instead of "Deutschland".

In any case, it is likely that "Hacan" follows at least vaguely regular English* pronunciation rules, or else the Federation would have spelled it differently.
 The fact that the Sol word for the Xxcha attempts to capture the sense of the word in the Xxcha language leads me to believe the same is true of the word "Hacan", meaning that "Hacan" being in the "Germany" category is unlikely (since it at least resembles the true pronunciation).  I would also contend that Hacaneese is different enough from future English that it is also unlikely to be in the "Shanghai" category since a near perfect phonetic analogue is unlikely to exist in English.  This means that the word is an English approximation of some lion word with a roar/grows in it, but is as concerned with having a regular English pronunciation as it is with mimicking the authentic pronunciation.

I think that "Ha - Kahn" would be the English word closest to the true pronunciation that is still consistent with the spelling and English rules of pronunciation.  There is precedent in English for a mid word "C" followed by an "a" to be pronounced "K" (ex. recap) and the hard C much more closely resembles a roar/growl than the soft "Ha- san".  I believe the A's have the same pronunciation as each other since this is still a reasonable English pronunciation that vaguely resembles lion noises.

* "English" being a stand in for "Future English or whatever other language the Federation of Sol uses"



Caveats:

We only have the Xxcha as the demonstration that "Hacan" is not in the "Germany" category.  We are also assuming that the language of the Federation closely resembles modern English, which it may very well not as even the same language changes a lot over thousands of years, so even if they use English, it may be a very different English (look up the Great Vowel Shift for an example of this).  Given these two things, you can make a case for basically any other pronunciation on the grounds that we use a totally different word from the one they use or that Federation pronunciation has migrated enough to defy our intuitions.  After all, Xxcha is a word that starts with a double "X", which no current English word does.