Pumpkin is Sayuri's childhood friend, and by "friend" we mean "person who doesn't treat her like dog poo." She's dopey, terrible at school, her tongue always sticks out, and she eats octopus off the ground. But beggars can't be choosers about who their friends are.
We often list things geisha aren't allowed, like boyfriends and comfortable pants. Friends are another one of these forbidden things. Life in an okiya is more about competition than it is about friendship, and Hatsumomo uses Pumpkin as her pawn in her war against Sayuri.
Pumpkin's big moment is when she betrays Sayuri by bringing the Chairman instead of Nobu to "accidentally" see her have sex with the Minister. Sayuri, as Sayuri is prone to do, feels betrayed without ever once thinking about how Pumpkin feels.
So let's do that. Geisha have terrible lives, and Pumpkin's is worse than most because, frankly, she's an idiot. As Mameha says to Sayuri, "Pumpkin fell short and you succeeded" (30.69). And now, having fallen short, Pumpkin is always playing second fiddle to Sayuri's charms. That has to be hard.
To be fair, Pumpkin gets revenge on Sayuri because "It must be hard for you to understand, Sayuri, when life doesn't work out perfectly!" (34.6). But life has hardly been perfect for Sayuri either. It seems that no geisha ever thinks about what others go through.