You do not need to nullify an adoption to change your name. Although I am not licensed in South Carolina, all states have a name change process that you can use that is fairly simple. In most cases, there are online forms.
Also, a step-parent adoption usually does not cut off inheritance rights from a biological parent, so a simple name change may be all that you need.
To eliminate any doubt, your biological father could always adopt you as an adult.
You should check South Carolina law.