TStyleManager does what you need to accomplish this task. Use TStyleManager.StyleNames to get a list of the styles, and TStyleManager.TrySetStyle to change them at runtime.
To see how this works, start a new VCL Forms Application. Add all of the VCL styles you want to the project, and drop a TComboBox on a form. You'll need to add the implementation uses clause like I have below:
uses
  Vcl.Themes;
procedure TForm1.ComboBox1Change(Sender: TObject);
begin
  TStyleManager.TrySetStyle(ComboBox1.Items[ComboBox1.ItemIndex]);
end;
procedure TForm1.FormShow(Sender: TObject);
var
  s: String;
begin
  ComboBox1.Items.BeginUpdate;
  try
    ComboBox1.Items.Clear;
    for s in TStyleManager.StyleNames do
       ComboBox1.Items.Add(s);
    ComboBox1.Sorted := True;
    // Select the style that's currently in use in the combobox
    ComboBox1.ItemIndex := ComboBox1.Items.IndexOf(TStyleManager.ActiveStyle.Name);
  finally
    ComboBox1.Items.EndUpdate;
  end;
end;