I say no, if you're talking about legislation. It's not that the parents don't have the right to know, but that if legitimate abortion doctors/clinics are required to inform parents, then the chances are that minor who do not want their parents to know will not go to a legitimate provider.
The risks and death rate involved in back-alley abortions, in my opinion, far outweigh the possible issues with someone getting an abortion that their parents don't know about. It seems to me that the open communication has to be fostered long before a minor is old enough to become pregnant, and if it hasn't been then there are many other -- potentially riskier -- behaviors that that minor is likely to be participating in without the knowledge of their parents.
Alternatively, if you're talking about case-by-case rather than actual laws -- yes, by all rights, this should be known to the family. Whether or not the family has the right to veto that decision is a topic for another debate, but it would give the opportunity for structured support from all parts of the family.