You can not do anything except file a correct tax return. If someone else that is not qualified to do so also files as Head of Household at your residence, the IRS will intervene. However, you can't and should not worry about what the other person does. As long as you are filing a accurate tax return, you should have zero issues when claiming your refund.
You can qualify for Head of Household if you:
If you were still legally married as of December 31, 2019 and a child lives with you, you can qualify for Head of Household under a slightly different set of rules. Read more
After you answer all the questions about yourself and your dependents at the beginning of your return, we'll let you know if your situation qualifies for Head of Household.
You can also revisit these questions by selecting My Info (online) or Personal Info (software), and then selecting Edit next to your name or your dependent's.