When you enter the form, it will ask you who the form is for - choose your spouse.   Or if you set-up a business profile for your husband' business, review it and make sure to mark that the business belongs to him and not you.   This is important because you want any self-employment taxes to be credited to the correct person.  

This did not work. The name reverted back to mine when I chose my husband's name as the recipient of the 1099-NEC. I backed out of the system and tried again. Same result. What should I do? I don't think IRS will allow me to take credit for his earnings due to a bug in TurboTax, right?

I'm having the same issue I believe this is a glitch with the software. I check my spouses name and it saves as my own. 

We appreciate you reporting this to us. Currently, there is a known issue where the spouse is not connected with the form should this be applicable to your situation. This link will allow you to add yourself to a list so that you can be notified when it is ready for use.

• Why am I not able to link the 1099-NEC to my spouse?

If you choose, you have the option of deleting the form and entering the income without the document. The entry is a convenience and not required by the IRS, you should keep the document with your tax files.

When you are signed into your TurboTax account follow the steps below.

1. Search (upper right) for Schedule C > Press Enter > Select the Jump to... link > Review
2. Select Business Income > Delete this form using the trash can beside the entry
3. Enter this as a cash payment of business income by selecting Other self-employed income, includes 1099-K, cash, and checks

[Edited: 02.02.2021 | 1:56 PST]

I'm not sure if you have resolved this yet but I found a fix that worked for me. I'm on the Deluxe download version of turbo tax so it may be a little bit different but I'll explain what I did to fix it. First input all the info that you normally would for the 1099-NEC if you are having the same issue I had it will revert your spouses name back to your own as soon as you click the next button. That's ok it will get fixed. On the deluxe download version there is a button at the top that says forms and it has an Icon that looks like a piece of paper click that. Scroll down until you see the 1099-NEC and click on it to open it. Then check the box on the form that says Spouse's 1099-NEC and it should automatically change the name to your spouse. Hope this helped!

@Gazpacho @ This solution (changing the actual form) worked perfectly. Thank you for sharing this workaround!