My divorce was finalized in 2001, should I still be filing as that status or single??

If you were divorced in 2001, you would file as single.  

If you are referring to 2021, you are considered unmarried based on your situation on the last day of 2020.

If you’ve never been married, or you’re legally separated or divorced on December 31, 2020, then you’re considered unmarried for the entire year.  Otherwise, you must file as married or married filing separately.  

"Divorced" is a marital status, not a filing status. Your marital status does not go on your tax return, but it helps TurboTax to ask appropriate additional questions as needed. When TurboTax asks for your marital status you should select divorced if you have not remarried. Subsequent questions will enable TurboTax to determine your filing status. If you have no children or other dependents, your filing status will be single.