try some thing like this
  while ( count < 3 ) // until three names are entered
{
   console :: write( " Please enter your name: ");
  Name[count].put(); ///like Name[count].gets()
   // person types in name
}

or either

CString temp;
char ch;
while(count<3)
{
console::print("Enter ur Name");
while(inner<10)
{
ch = getche();
if( "check for required input")
{
strcat(temp, toStr(ch);
inner++;
}
}
ch =  '\0'; \null  character
temp = "";
inner = 0;
}

Have a look at the Array class, all managed arrays inherit from this. It has copy functions and the like

Looking at your example, you've made a wrong assumption, or I have if "Name" means something else

Name[3] = {10,10,10}

This doesn't create 3 strings of 10 characters, it creates an array of 3 elements and each element is initialised with the value 10. When dealing with character strings you'll need to use an array of pointers

char* ptr[3] = {"Name1", "Name2", "Name3"}

This creates an array of 3 pointers to character strings, each one initialised to "Name#" respectively. The length of each element is set to the length of the initialiser

You don't have to initialise straight off though, you can do that when needed

char* ptr[3]

ptr[0] = new char[11];  // 10 for the characters and 1 for the '\0' terminator = 11

This is all low level stuff, from "C". .Net has classes for string manipulation, look at "String" and "StringCollection" classes for more examples

If you want some "C" style examples, checkout the "C" section at www.freshsources.com