It sounds like there is a lot to unpack here.
First, you must provide more than half the cost of maintaining our home for the entire year. To determine if this is true, you would have to add up all your housing costs for the entire year, including both when you lived apart and after you moved in with your fiancé, and determine if you paid more than half overall. That might be true but it depends on the relative cost of the accommodations. For example, if you lived in an apartment cost $500 a month, and you’re moved into your fiancé‘s penthouse which cost $10,000 a month, then your overall housing cost for the year was $500 times 10 months + $10,000 times two months, and you didn’t pay more than half the overall total.
Second, head of household does not just mean that you are the boss of your home, it is a special filing status that requires that you paid for and provided a home for a qualifying person, usually a child dependent. Do you have a child dependent who lived with you in the home that you provided for more than half the year?
Next, we have to think about your fiancé. Your fiancé can’t file head of household unless your fiancé provided half the cost or more of maintaining their home and paid for and provided a home for a child dependent. You can’t both claim the same child dependent. Furthermore, if your child dependent is not the biological child of your fiancé, your fiancé can’t claim the child as a dependent even if you were going to allow it. Does your fiancé have a qualifying dependent who is not your child?
So without more information about your dependence, it’s impossible to say whether you or your fiancé could actually file as head of household. Simply thinking about the question of did you provide “more than half“ the cost of maintaining the home where you lived, it could be possible that you provided more than half the cost of your home and your fiancé provided more than half the cost of their home, even though you moved in together toward the end of the year. You have to do the math.
