Can a child inherit from a father who is not the father named on her birth certificate?

Yes.
Legislation will vary according to country but anyone may inherit dependant on the will and testament of the deceased.
If the father is not the biological father he may still be the father in the eyes of the law. Should he have legally adopted the child for instance.
Yes.
Legislation will vary according to country but anyone may inherit dependant on the will and testament of the deceased.
If the father is not the biological father he may still be the father in the eyes of the law. Should he have legally adopted the child for instance.