There are several things. Assuming the US:
No, you cannot just make up a name and start using it in commerce.
One step you've got to do is create a legal entity for a fictitious name. That can be as simple as filing paperwork with the government for "Doing Business As", or it can mean incorporating. Two of the more popular are LLC and S-Corp. Any format can work, you'll need to do some homework about each. The rules vary by state, as do the way taxes work. There is also likely a Small Business Administration office near you (wherever you are in the US) and people at the office can help you figure out the government regulation side of things. You may also want to visit with a business lawyer for getting the paperwork in order. The fee varies by state, often in the $50 range but a few states are quite expensive.
Another thing you've got to do is ensure the rights are consolidated. This can be through a collaboration agreement, rights assignment, employment agreement, or other means. Otherwise you need to have unanimous approval for anyone to do anything with the product. Without it, any disagreement and the project is legally tainted. If anyone leaves the group (perhaps by moving, or maybe from a fight or even death) it can mean you project is permanently messed up from a legal perspective unless and until the rights are consolidated. If you've created a business entity like an LLC you would assign the rights to the entity. Otherwise you would assign the rights to the lead individual.
Once a single person or legal entity has the rights to the game, and the person or entity has a legal fictitious name, then you can use that fictitious name in commerce for distributing your game.
There will be several other things you should work through a lawyer. You will need to work over your product licenses, EULA, website terms of service, COPPA agreements, and possibly more. That is in addition to the legal documents in creating the entity's articles of incorporation and assigning rights of the people working on it, either as a collaboration agreement or other method. Some people balk at the cost of a lawyer. It is an absolutely necessary part of doing business. Shop around, the cost isn't as much as criminal defense lawyers and similar, often around $150-$200 per hour or so, and if you've done your homework and filled out as much as you can yourself, you can get most of it done in an hour or two where you're just looking for them to help you decide on filling blanks on standard forms they've already got in their drawer.
