I think they might. Maybe not all and always, but a thing about terrorists which can be quite mind boggling at times is that not everyone seems to agree who they are. Just look at how many countries are still doing business with Russia and other countries with less-than-stellar reputations. There may be plenty of parties who would actually not mind doing business with disreputable entities, for various reasons. I would assume they'd try to be a bit clever, but I wouldn't be surprised to see lax controls.

That's hilarious. "Payment of vest and explosives for ISIS attack"

Not really responding to your question, but one of my friend jokingly returned money to another friend with a bank transfer titled "for jihad". Needless to say, both banks were not amused. They both were "verified" on the phone and confirmed they are not, in fact, actually terrorists. I wonder how many people-years banks waste on pranks like this.

Many such organizations are legitimate legal entities in some country and handle purchases; and of course there are sanctioned people as well, and a payment from or to them does include their name.