Growing up we called these teepees (or tipis, the traditional term), but my guess is that whoever named this product wanted to keep it politically correct (interestingly in the Japanese version it’s also called キッズテント, or “kizzu tento”.
Of course there’s nothing shameful about the word “tipi” itself; it comes from a real, meaningful Native American dwelling. I think it’s okay to appreciate and enjoy these designs while also honoring the cultures they come from—both things can be true.
Tiny Land makes Teepee Tents that are very close to the Animal Crossing design, complete with the traditional shape and doorway in front and a little four-pane window on the side. It's made of thicker white cotton canvas fabric with thick solid wood poles. It's a great hideaway for kids from toddler age through elementary school.