Toad's first and last name is Toad so, just like Mario and Luigi. Something.
You might think Toadette is unlucky with her first name, but Toad naming schemes are notoriously uncreative or lame. Look at Toadsworth. Blue Toad's name is literally Blue Toad. Ditto Yellow Toad. Tayce T, Trini T, Faetalitt T., Zest T. Who names their kids that? Only Toads.