Isn't this considered a gentile's mistake, which is permitted?

And there isn't a desecration of God's name here?

I was asking from a halakhic perspective, not a moral one.
I would be glad for a halakhic source that forbids this, because I understood that halakhically a gentile's mistake is permitted.

In my opinion, from a halakhic standpoint (and not only a moral one), a gentile's mistake is forbidden. The permission was based on the way gentiles conducted themselves in the past. Gentiles today conduct themselves differently (certainly no worse than Jews). The Meiri wrote this in several places, and reason also supports it. If a gentile has ownership, that means others are forbidden to use his property without permission—not to rob, not to steal, not to deceive, and not to evade repayment of his loan, and so on.
You can see more about this in my article, "Is There an 'Enlightened' Form of Idolatry?"
Many halakhic decisors do not think this way, but in my opinion that is just conservative rigidity that causes them to cling to the sources literally without examining their relevance to our times.
And in any case where it could lead to a desecration of God's name, everyone forbids it, as is well known.

I already notified them yesterday that I received extra, because morally it wouldn't let me rest, and today I got a reply from them that because of the honesty they are waiving the surplus and I'll receive it without charge.

Does fairness generally pay off in life?

Thank you very much for the quick reply.

Very nice. Good for you.

Why notify them? And what if he doesn't want more than 8 units? Why should he have to pay for something he didn't order and doesn't need? They should pay him for shipping the items back. From my experience, that's a very complicated procedure.

Emmanuel,
In answer to your question, I own a factory and I will have future use for these products, so there was no reason to send them back, and in this situation I preferred to keep them with me.

Obviously, if I had no need for them, the discussion would be different.

Emmanuel,
I didn't say he has to pay for return shipping. I said he has to notify them. They will decide whether and how to take it back, at their expense of course. And if it isn't worthwhile for them, they'll leave it with him and he'll benefit from it (as in fact they did. I assume this wasn't only a reward for his honesty, but simply because it wasn't worth it for them to have the surplus returned).

Naor,
My discussion was דווקא on the assumption that you had no use for these items. If I had known that you also had use for the additional items, I would have told you to pay them. After all, you were going to order them in the future anyway, and at least you wouldn't lose out from using them.
However, now that you notified them and they waived it, you are under no obligation to pay.

Stiraaa commented, though not in the right place:
A gentile's mistake is forbidden because gentiles are decent now, so the reason for the law has lapsed.
So why not discuss whether the law should lapse because its reason lapsed? (The question was about a gentile who is a Torah scholar and upright.)

And here is my response.
Your intention is to ask: how can I cancel a law if its reason has lapsed? After all, this is something established by formal count and requires another formal count to permit it.
Now, we find in quite a few places that the medieval authorities (Rishonim) and later authorities (Acharonim) canceled a law when its reason had lapsed. See a survey in the third book of my trilogy, and more fully in the last chapter of Rabbi Neria Gutel's book The Changing of Natures. There are quite a few mechanisms for this matter, as I detailed there, and this is not the place to elaborate.
And in the present case, they permitted here the severe prohibition of theft, and it is obvious that once the reason lapsed, the prohibition returned to its place. There is no permission to harm a person's property without reason. And in the formulation of several later authorities (in other contexts) and of the Meiri in this very context: what they originally permitted was not "a gentile's mistake" in general, but "the mistake of a gentile who is not enlightened." See Maimonides' Commentary on the Mishnah on the Mishnah in Bava Kamma 37b and elsewhere.

Stiraaa meant something else, and commented in the right place. There the Rabbi said that a gentile is disqualified from serving as a judge, and did not say that this was only in their times, when gentiles were not bound by the norms of civilized nations, but that today a gentile who is a Torah scholar could judge like a Jewish Torah scholar. And on that basis Stiraaa found a contradiction in the Rabbi's words, because regarding a gentile's mistake he decided that this applied specifically in their times when gentiles were not restrained. The question is how one decides which law regarding a gentile still applies nowadays, and which law depends on his conduct and therefore no longer applies nowadays.

More power to you, Nelahav, for aiming exactly at my question.

All right, that really is a strange question, and I'll answer it there.