Blargy, your pawn looks like a bottle cap. So I suggest the new bishop be a vodka bottle indicating a wash up that can't walk forward straight, hence diagonal (but still straight) and needs to cap with the pawns once in a while. Now let's see if the neophytes find that hard to remember.
NEW Piece design COMPETITION
Look no further than some of the work by the great Doob...
https://www.chess.com/forum/view/general/exquisite-chess-set-hand-crafted-in-prison
Maybe have the pieces be political leaders, for example.
Trump as a rook, cause he likes walls and towers and stuff.
It DOES look pretty zen - like a tapestry or mural or similar - but I would spend most of the game trying to figure out which piece was which rather than thinking about actual chess moves...
Agreed, the Rook and Bishop need to have different shapes. Most of what helps us differentiate are shape and size. Those two have exact same shape and size from what I can tell. I suggest a shorter rook, and make it a rectangle.
If you need help, please contact our Help and Support team.

Okay, so, MY THINKING.
First, the rooks are towers, right? There are fewer better examples of the towering achievements of humanity than one of its greatest economic powerhouses: PepsiCo. As a bonus, the players will never get thirsty.
The knights are basically horses, and chess is supposed to be fun and magical, so I figure nothing enbodies the spirit of both fun and horse like Pinkie Pie. She's not suffering from any congenital defect, she just doesn't look her best so early in the morning.
Since chess is played in so many places by so many people of so many faiths (and a lack thereof), I wanted to replace the bishop with a symbol that's more universally relatable. With Erik's permission, I can reveal the true design, but I'll leave this placeholder for now and let the others demonstrate the quality you can expect from its design.
The king and queen both borrow lightly from the style used for Anglo-American playing cards. I added a tiny, transparent plastic piece to the bottom so they can stand up, freeing the players' hands for things like chess boxing.
For the pawns, I figure we could just use checkers. They're so cheap we can include, like, a dozen spares in every set. It's a statement on the transience and similitude of our lives that threatens constantly to drown our illusion of individuality, or something.