I was able to use the find function to find the quote's position, and then use copy to copy the name.
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tester="\"";
findPos=line.find(tester); //finds first quote mark
findPos2=line.find(tester, findPos+1); //finds second quote mark
length=line.copy(name, (findPos2-findPos-1), findPos+1); //copies the name into name
name[length]='\0'; //end it off
cout<<"Name: "<<name<<"\n";