for (int i = 0; i < number; i++)
{
   Customer stringArray[i] = new Customer();
}

using System;
using System.Collections.Generic;
using System.Linq;

namespace ConsoleApplication5
{
    class Program
    {
        static List<Customer> customers;

        static void Main()
        {
            // let's say these are the names in a string array
            String[] names = new String[] { "david", "john", "peter", "andrew", "simon" };

            // why not have a list of Customer objects and include
            // the customer's name within the Customer object
            customers = new List<Customer>();

            // initial population of the list
            foreach (String str in names)
                customers.Add(new Customer(str));

            // example of finding a customer's object
            Customer test = GetCustomer("david");

            if (test == null)
                Console.WriteLine("customer doesn't exist.");
            else
                Console.WriteLine("customer exists!! :-)");
        }

        static Customer GetCustomer(String CustomerName)
        {
            var query = from x in customers where x.CustomerName == CustomerName select x;

            if (query.Count<Customer>() > 0)
                return query.ToArray<Customer>()[0];

            return null;
        }
    }

    class Customer
    {
        public String CustomerName;
        // adding the rest of your object variables and methods here



        public Customer(String CustomerName)
        {
            this.CustomerName = CustomerName;
        }

        public override bool Equals(object obj)
        {
            // give the Equals method a proper purpose
            return this.CustomerName == ((Customer)obj).CustomerName;
        }

        public override int GetHashCode() { return base.GetHashCode(); }
    }
}