Yes, you can amend a tax return to change your filing status from Single to Head of Household, if you are eligible for the HOH filing status.
See this TurboTax support FAQ for Head of Household - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-filing-status/qualify-head-household...
Note - If you amend a 2020 return and it has a tax refund, the refund will not be paid since it is beyond the 3 years from the due date of the 2020 tax return.
See this TurboTax support FAQ for amending a prior year tax return - https://ttlc.intuit.com/turbotax-support/en-us/help-article/tax-return/amend-change-correct-return-a...
