Do I need to update address on ID before filing Head of Household?

Your ID address doesn't need to match your current address for tax filing purposes. The IRS is concerned with where you actually lived and maintained a household, not what's on your license. Just make sure you can prove you lived at the address you're claiming (utility bills, lease, etc) for more than half the year.

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i filed HOH last year with old address on ID, no problems here

your actually supposed to update your ID within 30 days of moving in most states but nobody really does lol

Better question is do you qualify for HOH? Make sure you meet all requirements - supporting someone, paying more than half household costs, unmarried etc

Just to add to what others have said - the IRS cares about your actual residence, not your ID address. But definitely keep good records like lease agreements, utility bills, bank statements showing your address, etc. If you get audited, you'll need to prove you maintained the household at that address for more than half the year. The documentation is way more important than what's printed on your license!