According to the main site, Totodile, Phanpy and Houndour can Dynamax, but whether that’s an error or not is unclear, but if it was an error, Totodile wouldn’t be listed as being able to Dynamax on the main site. Yes, I did my research and confirmed that they apparently can be transferred to Sword and Shield.
Are you sure about that? Because I just tried bringing a Houndoor and a Totodile into Sw/Sh and Home actively blocks that transfer. Home says that the Pokémon can’t be transferred into the game. If you've done it, then please share some screenshots of a Dynamaxed Totodile being used in Sword or Shield.
I think you're referring to the Serebii Online Dex for GenVIII. It says that any Pokemon in GenVIII can Dynamax, even those Pokemon that aren't found or can't be brought into Sword and Shield. That is because, AFAIK, all playable Pokemon in Sword and Shield can Dynamax or Gigantimax. You have to scroll down a little bit further to the
Locations and
Flavor Text sections to see that Sword, Shield, and the two DLCs are not listed in the entries for Totodile, Phanpy, or Houndoor. These Pokemon are only listed in the GenVIII Pokedex because they appear in BDSP.
Compare those Pokemon to Squirtle. Squirtle is also listed as being able to Dynamax, and if you go to its
Locations and
Flavor Text sections, you'll see that it shows that it can be transferred into Sword and Shield through Home and has a Pokedex entry.