Hi Dharmender,
Below code works for me 
I have created parameterized DBcontext with Dbconnectionstring Parameter, in this way we can pass connection string before binding Customer Data.
DBcontext  class  for customer 
public class CustomerDbContext: DbContext
{
    public CustomerDbContext(string databaseConnection)
      : base()
    {
        ConnectionString = databaseConnection.ToString();
    }
    public string ConnectionString { get; set; }
    protected override void OnConfiguring(DbContextOptionsBuilder optionsBuilder)
    {
        optionsBuilder.UseLazyLoadingProxies(true).UseSqlServer(ConnectionString);
    }
    public DbSet<Customer> Customer { get; set; }
get Method in Repository class 
private CustomerDbContext _contextFactory;
public List<Customer> GetCustomer(string databaseName)
{
    _contextFactory = new CustomerDbContext(databaseName); //first set the connection string 
    return _contextFactory.Customer.Select(p => this.mapper.Map<CustomerResponse>(p)).ToList(); //Bind data from provided server
}