The planet Hain is referenced in numerous books of Le Guin's Hainish cycle.

I always imagined it would rhyme with "rain" but I've recently heard it pronounced more like "hay - een" on an audiobook.

Is there any definitive information for how it should be pronounced?

According to Ms. Le Guin on herself,

How do you pronounce the names and words in your books?

You the Reader have Reader’s Rights. One of them is to pronounce made-up names and
words the way you want to.

But people do like to know how the maker-up pronounces them. And since
this does affect the sound and rhythm of a sentence – and since names
are magic in Earthsea – here are some guidelines. In my invented names
and words, usually:

A is ah

E is eh

I is ee

O is oh

U is oo

EY rhymes with they

AY rhymes with either they or high

All the E’s are pronounced, including final e: Meshe = mesheh.

You have to take your chances with G, but usually it’s G as in get,
not G as in gem. So Ged is Ged not Jed, Ogion rhymes with “bogey on.”

(A couple of names in Left Hand are pronounced as if in English: Tibe
is not tee-beh, but rhymes with bribe. Karhide sounds like two English
words, car-hide.)

Where to put the stress? No general rule. (Yeowe is yeh-OH-weh, not
YOWie!)

Don’t worry about it. Say things they way they sound good to you.

Or you could get one of the audio recordings of the book. As a rule
the producers and performers take great care to check the
pronunciations with me.

So, it would seem that you can take the audiobook you listened to as correct.

It would also be arguable, using the guide above, that it would rhyme with "mine", rather than "rain".

And it's also arguable, using the "Reader’s Rights" clause, that it does in fact rhyme with "rain" - for you.

Hein (like mine), not Hain (like rain).

In a footnote to the excellent Coyote's Song: The Teaching Stories of Ursula K. Le Guin, Richard D. Erlich mentions that he's spoken to Le Guin on several occasions about the pronunciation of the word Hain. In short, it's closer to the French word 'hein' than the word 'rain'.

Le Guin and I have corresponded, somewhat flippantly, on the meaning of Hain. Le Guin would have it pronounced [hain], with the option of rendering the n somewhat nasalized, French fashion, making the word similar to the French word hein ("Eh?").

Hain is also the brand name of a line of natural-food products; in correspondence in July 1989, Le Guin told me 'we have been using Hain(ish) Mayonnaise for years'; in a note in 1996, however, she said that she had not known about Hain condiments (etc.) when she first used the name.