You're a partnership. You should ask the money to be paid to the partnership. You'll have to fill partnership income tax return (form 1065) and each of you will get a K-1 schedule with your own personal portion of the income.
For example, you're Adam, Ben and Clara. You work together on a project and are being paid. You get a check for $300 issued to "Adam, Ben and Clara, DBA ABC Partnership". You don't have to have a DBA, it just makes it easier to show you as a single entity.
You then deposit the check to an account you set up for your partnership, and from that account you transfer $100 to each of you.
Year end, you file form 1065, showing $300 income, and attach K-1 for each of the partners showing $100 income. That $100 income will flow to your individual tax returns.
The overhead here is setting up a partnership account, potentially making a DBA, and filing the extra tax return.
That's the proper way to do it, especially if it is something you're going to do regularly.
For a one-time thing, one of you can get paid, report it as income on his/her Schedule C, and issue 1099 to the rest of you for your parts, and deduct the amount as his/her expense.
Here, the overhead is Schedule C for each of you (instead of Schedule E if handling it as a partnership), extra 1099 forms (instead of 1065 and K-1s), and a risk of one partner defrauding the others (depends on how much you trust each other).
With proper documentation, each of these is equally legal, and tax-wise the costs are the same (i.e.: either way you pay the same taxes). With partnership the overhead is a bit more expensive (DBA+1065 extra cost), but in the long term it will make your life easier if you do this kind of thing regularly.
You may want to consider setting up your partnership as a LLC/LLP (depending on what your State allows), but that would require State paperwork and potentially more fees.