I received multiple 1099-NECs for payments issued to me in December but not received by me until January. How should I deal with this?

You have a legitimate question, but the answer will require a decision.

The companies you worked with are probably on an accrual system.  This means that when they got your bill they registered a payment and generated the 1099-NEC.  If you were on an accrual basis (which you're not) you would have recorded payment when you sent them the bill originally.  All would be well, but that's not the way it is.

You are on a cash basis which means you take credit for the money when you receive it.  The two systems are in conflict, but neither is wrong.  The companies probably will not change their accounting system and issue new 1099-NECs.  

This is your decision:

• Do you post the income to 2021 as the companies reported it, and adjust your books to reflect the money coming in earlier?
• Or, do you not post the 1099-NECs in 2021 (with the intention to post it in 2022) and endure the IRS questioning about the missing information.