Two options. First, escape the quotation marks so the shell doesn’t eat them:
gcc -Dname=\"Mary\"
Or, if you really want -Dname=Mary, you can stringize it, though it’s a bit hacky.
#include <stdio.h>
#define STRINGIZE(x) #x
#define STRINGIZE_VALUE_OF(x) STRINGIZE(x)
int main(int argc, char *argv[])
{
printf("%s", STRINGIZE_VALUE_OF(name));
}
Note that STRINGIZE_VALUE_OF will happily evaluate down to the final definition of a macro.