You have one domicile. Your domicile is your real and permanent home. There are a number of factors that determine where your domicile is, and without discussing all of them, one of the factors is that you intend to return after a temporary absence. You can maintain your domicile in one state and be temporarily away for an indefinite period of time as long as you maintain that permanent residence and your intention to return.
You are generally required to file a resident tax return in the state where you maintain your domicile, that reports and pays income tax on all your worldwide income. Your home state should give you a credit against taxes paid in another state, which reduces the impact of double taxation.
If you temporarily live and work in another state, you are generally a non-resident of that state, and you would file a non-resident tax return that only reports income earned from or sourced to that state.
Virginia is one of several states that includes a definition of statutory resident. This is someone who maintains an abode in Virginia for more than 183 days, even if their permanent home or domicile is not in Virginia. The definition of abode can vary from state to state, but it generally means that you live in a house, an apartment, or other permanent structure, that has all the characteristics of a home (bathroom, bedroom, kitchen, etc.). Abode does not usually include hotels or camping. If you are a statutory resident of Virginia, you are required to file as a Virginia resident. This makes you a resident of two states (rather than a non-resident), and it complicates a person's state income tax situation.
If you are not living in Virginia more than 183 days of each calendar year, or if you are staying in a hotel during your temporary stay, even if it is longer than 183 days, then you are not a statutory resident, and you would file as a non-resident.
From the VA instructions:
Resident -- A person who lives in Virginia, or maintains a place of abode here, for more than 183 days during the year, or who is a legal (domiciliary) resident of the Commonwealth, is considered a Virginia resident for income tax purposes.
Here is the actual law,
https://law.lis.virginia.gov/admincode/title23/agency10/chapter110/section30/
