uses

  Androidapi.Helpers;

function PackageName: string;

begin

  Result := JStringToString(SharedActivityContext.getPackageName);

end;

Reading iOS bundle name:

uses

  Macapi.CoreFoundation, iOSApi.Foundation;

function PackageName: string;

begin

  Result := TNSString.Wrap(CFBundleGetValueForInfoDictionaryKey(CFBundleGetMainBundle, kCFBundleIdentifierKey)).UTF8String;

end;