Yes, you should use the same filing status for all jobs that you work this year. When you file your 2022 tax return you would file as Head of Household as long as you meet the requirements. Here is some information for how to qualify as Head of Household:
All the best!
AnthonyC_CPA
Do I have to make any changes on my W-4 with my primary, full-time employer to indicate I have a part-time job?
You do not have to make any changes on the W4 with your full-time employer related to the part time job. However if your income from your part-time job is going to raise your taxable income to a higher tax bracket you may want to check if you are having enough federal and state taxes withheld so that you don't owe income taxes when you file your 2022 tax return.