Mom is in a nursing home, taxes were in dad's name. He is now deceased, should I put taxes in mom's name?

There should have been a final tax filed for dad. How long ago did he pass? From his final tax forward, taxes would be in mom's name.

This is sticky and you need a lawyer. If Mom is in a NH under Medicaid she can't pay taxes, upkeep, or utilities on a house. If money was left to her, Medicaid will stop and she will have to spend down and then file for Medicaid again. If she is private pay and may need Medicaid, she can't pay bills on a house. All money goes to her care. I would leave taxes in Dads name. Probate and then sell the house unless someone wants to pay for upkeep.

Taxes for what? Property taxes? Income tax? Help us to help you.

I imagine your mom inherited everything after your father's death? The taxes follow the owner, and the ownership issues should have been settled as part of the estate settlement.