Can an unmarried couple living in the same house have one person claim head of household while other claims the dependent

Unfortunately, if you are unmarried and lived in the same household, only one of you can file as Head of Household AND claim the dependent. The other has to file as Single.

To file as Head of Household, the conditions are that you must claim a qualifying person as a dependent AND have paid more than half the cost of keeping up a home for the year.

Therefore, both of you cannot claim to have paid more than half of the cost of keeping up the same home.

The best solution tax-wise would be for the person with the higher income to claim the dependent and file as Head of Household.