procedure TForm1.Button1Click(Sender: TObject);
begin
  ShowMessage(ComboBox1.Items[ComboBox1.ItemIndex] + #13 + Integer(ComboBox1.Items.Objects[ComboBox1.ItemIndex]).ToString)
end;

procedure TForm1.FormCreate(Sender: TObject);
var
  Item: TPair<Integer, String>;
begin
  List := TDictionary<Integer, String>.Create;

  // Test base
  for var I := 0 to 10000 do
    List.add(I, 'Name_' + I.ToString);

  // ...
  for Item in List do
    ComboBox1.AddItem(Item.Value, TObject(Item.Key));
end;

procedure TForm1.FormDestroy(Sender: TObject);
begin
  List.Free;
end;

unit Unit1;

interface

uses
  Winapi.Windows, Winapi.Messages, System.SysUtils, System.Variants,
  System.Classes, Vcl.Graphics,
  Vcl.Controls, Vcl.Forms, Vcl.Dialogs, Vcl.StdCtrls,
  System.Generics.Collections;

type
  TForm1 = class(TForm)
    ComboBox1: TComboBox;
    Button1: TButton;
    procedure Button1Click(Sender: TObject);
    procedure FormCreate(Sender: TObject);
    procedure FormDestroy(Sender: TObject);
  private
    List: TDictionary<Integer, String>;
    IndexArr: array of Integer;
    { Private declarations }
  public
    { Public declarations }
  end;

var
  Form1: TForm1;

implementation

{$R *.dfm}

procedure TForm1.Button1Click(Sender: TObject);
var
  idx: Integer;
begin
  if ComboBox1.ItemIndex <> -1 then
  begin
    idx := IndexArr[ComboBox1.ItemIndex];
    ShowMessage(idx.ToString + #13 + ComboBox1.Items[ComboBox1.ItemIndex]);
  end
  else
    ShowMessage('Выбрать элемент! Я есть Элемент.')
end;

procedure TForm1.FormCreate(Sender: TObject);
var
  Item: TPair<Integer, String>;
  i: Integer;
begin
  List := TDictionary<Integer, String>.Create;

  // Test base
  for var v := 0 to 10000 do
    List.add(v, 'Name_' + v.ToString);

  SetLength(IndexArr, List.Count);

  // ...
  i := 0;
  for Item in List do
  begin
    ComboBox1.Items.add(Item.Value);
    IndexArr[i] := Item.Key;
    inc(i);
  end;
end;

procedure TForm1.FormDestroy(Sender: TObject);
begin
  SetLength(IndexArr, 0);
  List.Free;
end;

end.