/**
没有const。
char *name;
**/
#include <iostream>
#include <cstring>
using namespace std;

class Student
{
public:
    Student(int n,char *na,float s):no(n),score(s)
    {
        name=new char[strlen(na)+1];
        strcpy(name,na);
    }
    Student(const Student& s):no(s.no),score(s.score)
    {
        name = new char[strlen(s.name)+1];
        strcpy(name,s.name);
    }
    ~Student()
    {
        if(name!=NULL)
            delete []name;
    }
    void display()const
    {
        cout << no << " " << name << " " << score <<endl;
    }
protected:

private:
    const int no;
    char *name;
    const float score;
};

int main()
{
    const Student stu1(1,"wangming",99);
    stu1.display();
    const Student stu2(stu1);
    stu2.display();
    return 0;
}

/**
包含const。
const char * name;
**/
#include <iostream>
#include <cstring>
using namespace std;

class Student
{
public:
    Student(int n,char *na,float s):no(n),score(s)
    {
        name=new char[strlen(na)+1];
        strcpy(name,na);
    }
    Student(const Student& s):no(s.no),score(s.score)
    {
        name = new char[strlen(s.name)+1];
        strcpy(name,s.name);
    }
    ~Student()
    {
        if(name!=NULL)
            delete []name;
    }
    void display()const
    {
        cout << no << " " << name << " " << score <<endl;
    }
protected:

private:
    const int no;
    const char *name;
    const float score;
};

int main()
{
    const Student stu1(1,"wangming",99);
    stu1.display();
    const Student stu2(stu1);
    stu2.display();
    return 0;
}

class Foo {
    private:
        const char *name;
    public:
        Foo(const char *name) : name(name) {}
        Foo(const Foo &other) : name(other.name) {}
        void show() const {
            cout << this->name << endl;
        }
};

如果一定要给字符串分配内存, 那就这样

class Foo {
    private:
        const char **name;
    public:
        Foo(const char *name) : name {new const char * {name}} {}
        Foo(const Foo &other) : name {new const char * {*other.name}} {}
        ~Foo() {
            delete this->name;
        }
        void show() const {
            cout << *this->name << endl;
        }
};

设计错误
如果你想定义一个不可修改的对象，那应该是定义 const Student 就行了，而不是定义一个内部全是const成员的Student.
当然，你一定要这么做也可以，和其它成员同样方式处理，即放到初始化列表中

#include <iostream>
#include <cstring>

class Student
{
public:
    Student( int no, const char* name, float score ) : no_(no), name_(strcpy(new char[strlen(name)+1],name)), score_(score)
    {
    }
    Student( const Student& s ) : no_(s.no_), name_(strcpy(new char[strlen(s.name_)+1],s.name_)), score_(s.score_)
    {
    }
    ~Student()
    {
        delete[] name_;
    }

protected:
    Student& operator=( const Student& s );

private:
    const int no_;
    const char* name_;
    const float score_;

    friend std::ostream& operator<<( std::ostream& os, const Student& s )
    {
        return os << s.no_ << ' ' << s.name_ << ' ' << s.score_;
    }
};

using namespace std;

int main( void )
{
    Student stu1( 1, "wangming", 99 );
    Student stu2 = stu1;
    cout << stu1 << '\n';
    cout << stu2 << '\n';
}