If your mother earlier signed a durable power of attorney for property management naming someone to act as her agent with respect to property upon her disability, that agent can
If your mother did not sign such a document and is unable to sign legal documents at this point, because she can no longer understand what she is signing, you would need to have someone named as her conservator, also called an adult guardian is some states, who is authorized by the court to act on her behalf with respect to property, her medical affairs, or both.
Such a conservatorship is a formal court procedure that limits someone's legal rights, and it is often time consuming and expensive process in most states. Most people hire attorneys for help through the process, but check with the probate court in your county to see what self-help resources it provides.
If you want to change the name on the deed because of Medicaid eligibility in your state, though, you would be wise to consult an experienced elder law attorney first. Such transfers will have tax consequences that may outweigh the benefits of the transfer for eligibility purposes.
transfer the property to your dad's name alone.