EIther way is fine as long as all the details are correct with the rest of the 1099's, like EIN and addresses. Yes, you are correct, the names should be updated this year.
Please see this resource for deadline updates:
The Tax Deadline Delayed: What to know about Coronavirus COVID-19 and your Taxes and State Tax Updat...
[Edited 3/24/2020 | 10:56 AM PST]
@cp5491r
