For those unaware, IRL Deep Impact's nickname was Pui. (from Dhiipu Inpakuto.)

Which also happens to be onomatopoeic for a guinea pig's "wheek" in Japanese.
(Yeah, so Pui Pui Molcar is effectively Wheek Wheek Cavycars.)

NNescio said in comment #2595776:

For those unaware, IRL Deep Impact's nickname was Pui. (from Dhiipu Inpakuto.)

Which also happens to be onomatopoeic for a guinea pig's "wheek" in Japanese.
(Yeah, so Pui Pui Molcar is effectively Wheek Wheek Cavycars.)

Based on JP testimonials the Pui nickname didn't seem to have spawned until much more recently though. Contemporary JP keiba fans called him "Deep" from what I can tell.