Is there any way to form an anonymous General Partnership?

I would suggest that you might want to pay a CPA to assist you in filling this document out (for the first time, anyway) as they generally have a very detailed understanding of the law and your obligations. But if you really prefer to do this yourself, you should read the IRS's instructions for form 1065 (which are quite long but very detailed and may be helpful if you're unsure what to put for a specific item). Be sure to scroll down or use the table of contents on the left, as the top part of that page is a listing of everything that has recently changed (which you likely don't need to care about, at least for your first time filing). It then goes on to give both general and specific instructions for the form, which is probably what you want to be reading.

Now, to your specific questions:

Is there any way to do this anonymously?

Heck no. Each partner will need to provide all of their personal information on a copy of Schedule K-1, which must be attached to Form 1065. Your real-world identities will be associated with this partnership, and with each other, like it or not.

Depending on how much you're willing to spend on this, you may be able to hire a lawyer, CPA, or tax preparer to act as a third-party intermediary. They would receive Schedule K-1 from each partner, compile the whole thing together, and then submit it to the IRS. As a result, you would be able to keep your identities secret from each other. If you're going to consult a CPA anyway, you may want to ask if this is a service they are willing to offer, or if they can give you a referral to someone who can do it.

[D]o I have to tell the government I am making a NSFW game?

Probably not. You have to list your "principal business activity" and "principal product or service," but the former is just a matter of picking a code out of this list, and the latter can (probably) just be "video games" or similar (assuming you call yourself a "software publisher"). They don't actually want to know what kind of game you're making. They just want a general category of business. In the event you get audited, they might ask you to demonstrate evidence for all of your business expenses, and in principle, they might also ask you to demonstrate evidence of revenue, but this is usually just a matter of showing them paystubs, invoices, etc. I would be rather surprised if they wanted to see the actual game itself, although I suppose anything is possible if (for whatever reason) they suspect you of committing fraud.

Regardless, it is very unlikely that the government will care that you're making an NSFW game. NSFW products are a big business, and perfectly legal (in most cases). It's much more likely that your bank will care.

Are they also going to file a form 1065?

No, the partnership files one for both of you. That means either you file it, or they file it, not both. But you will (probably) both need to both fill out schedule K-1 as discussed above.

I think the core point is that the Government needs a person and address, so they can contact you (to go after you for taxes, etc.). Therefore, anonymity to the government is not possible.

However, you can go to a lawyer, and contract him to act in your both names founding a trust*, and give his address and name as a contact on the company (the company would be owned by the trust).
This way, the government has a contact point, and the contact point (the lawyer) is responsible for the company paying taxes, and is keeping your identies hidden. The lawyer in turn knows your data, and forwards the tax filings etc., and knows how to find you.

[*trust might not be the proper term]

Both of us want to remain anonymous and don't want to even tell each other each other's names. Is there any way to do this anonymously?

Yeah. Fire up those Wyoming LLCs.

An LLC can be a general partner.

It's perfectly legitimate to have a general partnership between "New Start Flying Wings LLC" and "Not Slightly From Wyoming LLC".

Note that you'll have to jazz up your LLC a little bit in order to keep it from being a "Single Member (pass-through) LLC", which in the IRS's eyes is a "disregarded entity". Have a second Member, or elect corporate tax treatment.

Anonymous might be the wrong word: do I have to tell the government I am making a NSFW game?

IRS doesn't care whether your game is a Pac-Man knockoff or Solitaire or one of those city building games or whatever.

However DOJ cares about porn. So you need to keep an eye on the trends in porn regulations and practical enforcement. Generally USA porn laws give a light touch to porn that doesn't involve real actors, but there's still an obscenity "line" you should not cross. And it's anyone's guess where that line is, because DOJ intentionally leaves the industry guessing as to what they consider obscenity. For instance (live) bondage producers mostly stuck to gentle loving bondage until Insex broke a bunch of taboos and mostly got away with it. Other producers tested sexual intercourse in gentle bondage, and the bar moved again. There's no published guidance as to what content is allowed; just a series of taboos. It's 50 shades of grey.

So you want good porn lawyers to help guide you.

Do I need to know my partner's personal information to fill this out?

You'll need to know your partner's LLC's name, EIN and Wyoming registered agent address to fill the 1065 out (or to be more precise, the K-1 forms which are part of the 1065).

What form does my partner need to fill out? Are they also going to file a form 1065?

The partners don't file multiple Form 1065s. The partnership files one. It lists all partners (again: these partners can be LLCs).

The answer is simple in my opinion: Don't form a General Partnership with someone you barely know on the internet.

The General Partnership is something that makes it easier to start a small business with multiple people who completely trust each other, like maybe a farm run by the whole family unit, or a store run by two close friends. A counter example would be a tech start up founded by a couple of university students, usually that's already too large and unpersonal to be suited for a General Partnership.

If you form a General Partnership, you and the artist both can make decisions for the company, alone, and both are fully liable not just for your own actions but also for the other's actions.

The top voted answer on your other question suggests a vendor-buyer relationship and that's exactly what you should do to keep things simple and separate. The difference to a General Partnership is mainly wording: You don't have a joint business, you have two businesses which are closely linked. The game company tells the art company what art they need, the art company provides art in exchange for half the profit.

Of course there might be more back and forth going on, and you don't need to be a dictator about the evolution of the game, but no one at the IRS cares about that, that's just customer service the art company provides, or whatever. If the venture takes off and the artist also wants a more formal share of the company, then you can still form a formal business together, but then probably not a General Partnership but rather a "Corporation" or something - as far as I can tell a corporation is the USA equivalent of the "Société anonyme" that exists in Europe in one form or another and literally means anonymous corporation for good reason.

To answer your specific question, that hasn't been answered:

Is there any way to do this anonymously?

Yes, you can give it away for free instead of selling it.
Otherwise, you'd better have your ducks in a row.

Maybe that advice about Wyoming LLCs will work, but from what I've seen people tend to figure out more than you'd expect.