You don't declare a primary home on your tax return. The address that you enter on your federal tax return is a mailing address where you want the IRS to send anything that they might mail to you. It does not have to be your primary home.
If you claim itemized deductions you can deduct mortgage interest on your primary home and one other home. If you deduct mortgage interest on two homes, it doesn't matter which one is your primary home. You can deduct real estate tax on any property that you own in the United States, whether or not it's your primary home.
If you sell a home, your eligibility for the Section 121 exclusion of gain depends on whether the home that you sold was your primary home for 2 or more years out of the 5 years preceding the sale.
If your two homes are in different states it might affect your state taxes. Some states have tax benefits of various kinds for homeowners, which might depend on whether a home is your primary home. You would have to check the rules for your state.
In general, which home is your primary home is going to be determined by facts and circumstances. It's not something you can declare or choose. The rules for determining your primary home might be different for different tax considerations and for different states.
