It depends. If the person is eligible to be claimed as a dependent on your 2019 tax return, then "No" you should not amend because that person is only eligible to receive the $500 payment for a dependent.
If the person is not eligible to be claimed as a dependent on your 2019 tax return, then "Yes" you should amend to correct the 2019 tax return you filed.
Table 5 from IRS Publication 501 at this link is a good overview of what it takes to claim a depende....
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