If I own a home with someone that is not my spouse can we both write off the mortgage, taxes and insurance? Both of our names are on the 1098.

It depends on whether you are both making payments. If the Form 1098 has both your names and both of you are paying the mortgage/interest, each of you can deduct your portion of the interest paid. When entering the Form 1098 only enter the amount that you actually paid, not the full amount. This TurboTax Help article outlines some of the situations when co-owning a home.  Deduct Mortgage Interest if Co-own Home

When you come to the page in the Home Mortgage Interest section that says Do any of these uncommon situations apply to your loan with The Lender? check the radio button for Someone who isn't my spouse co-owns this loan, and we only pay a portion of it. This will open up another question and help you enter the form.
 

You can each deduct what you actually pay.  Don't deduct more than the total between you.