I needed an NPC to combine a magic item shop and magic weapon shop. I thought it'd be funny if an NPC for each half of the shop was each head of an Ettin, but then remembered their INT score. That lead me to think: How would an Ettin work with a Headband of Intellect? Would they need two to gain the INT score boost? If they only had one, would only one of the heads gain the boost to their intelligence?

I asked one of my friends, and they said that one was enough for both of them (because technically they're the same creature) but that it'd be funny to play one of the heads as super smart and disgusted at the others stupidity though.

RAW: it takes one, which can be worn by either head, as it's one creature with one Int score, regardless of the head count. This will be true for anything with multiple heads but a single statblock, like a hydra, for example.

RAF: the heads have some individuality and you can RP it however you want: the Int score goes to 19 for saves and mechanical purposes but only the wearer actually uses that intelligence and sounds smarter than the 'dumb' head which will still be RP'd as if the original int score.

Maybe they fight over the headband, one of them is a more generous shopkeeper while the other is a miser.

It's an NPC, and not one the PCs are meant to fight either. That's pretty much a licence to do whatever you want with it. I say go nuts. All of the ideas above are great. Maybe it's a half--ettin, half something else and it's already a tiny bit smarter because of that. Maybe it's possessed, by two different entities that occasionally try to oust the other one to get the whole ettin to itself. Maybe the item that boosts its Int randomly changes which head it goes for every day. You have something of a rough gemstome here, just waiting to get cut and polished.