Invoke ReSharper for the rename if available.

[JohanLarsson]

protected override Action<ITextControl> ExecutePsiTransaction(ISolution solution, IProgressIndicator progress)
{
  return (Action<ITextControl>) (tc =>
  {
    string str = RenameRefactoringService.Rename(solution, new RenameDataProvider(this.myElement, this.mySuggestedName), tc);
    if (str.IsNullOrWhitespace())
      return;
    BulbActionBase.ShowTooltip(tc, str);
  });
}

Roslyn rename is pretty much break code as a service.