If you are legally married and living together then you can only file a US tax return as either Married Filing Jointly or Married Filing Separately.
If you are not legally married then you can only file your tax return as Single.
You can file as Head of Household if you are single and eligible - https://ttlc.intuit.com/community/family/help/do-i-qualify-for-head-of-household/01/25539
You may be able to file as Head of Household if you are married and eligible - https://ttlc.intuit.com/community/married/help/can-a-married-person-claim-head-of-household-filing-s...
