Just changing the child's name to the stepfather's is commonly known as a "back alley adoption".

You see, if the child has the name of the stepfather, the stepfather has an assumed right to make decisions on behalf of that child (medical care, school, etc).

That is not correct.

Have the stepfather adopt or leave things as they are. The step father is a legal stranger to the child up to the moment the adoption is finalized. Changing names to try to circumvent the process is not a good idea... especially when you will have to explain to a judge later why the father's rights are being suppressed.