The WILL given by your mother will take effect only after the death of your mother. It has no effect when your mother is alive.
It is not clear as to what is written in the Power of Attorney. Only after completely going through the contents of the Power of Attorney one will be able to say anything.
In any case, if the Power of Attorney gives power to change the property from the name of your mother to your name, then to change the name, you have to prepare necessary transfer deed by consulting a lawyer, and you also have to pay STAMP DUTY (which is payable on the value of the property) and registered with the Sub-Registrar's office.