Here's where Amos Burton's "Peaches" nickname for Clarissa Mao comes from in The Expanse. One of the very first true villains in The Expanse, Jules Pierre Mao was responsible for inhumane and foolhardy attempts to weaponize the Protomolecule, using kidnapped children as test subjects. Jules was brought to justice thanks to James Holden and the Rocinante crew, and this left the mad scientist's daughter, Clarissa Mao, with an ax to grind against The Expanse's protagonist. Ultimately, Clarissa saw the error of her ways, realized Holden wasn't so bad, and got sent to jail.
Clarissa Mao briefly returned in The Expanse season 4, fostering a connection with Amos Burton from her cell on Earth. It's during this initial exchange that Amos signs off with "sure thing, Peaches" and the new nickname clearly catches Clarissa off guard. Amos finally visits his long-distance pal in person in The Expanse season 5, still referring to her exclusively as "Peaches."
Amos' source of inspiration for this nickname and his reason for using it are two entirely separate things. "Peaches" is a play on Clarissa's alias in The Expanse season 3. Before being outed as the vengeful daughter of Jules Pierre Mao, Clarissa went undercover as Melba Koh in order to exact her revenge on Holden. When she later contacts Amos from jail, he answers with "Melba?" and she corrects him, saying "please, Clarissa." Of course, Amos ignores her request and opts for Peaches instead. This is inspired by Clarissa's former pseudonym, with peach melba being a famous dessert comprised of peaches and ice cream.
However, the Clarissa's new moniker is far more than just a simple pet name for someone Amos is fond of. Amos wants Clarissa to let go of her past, stop punishing herself for past crimes, and find a way to move on. Once Amos decides to be Clarissa's knight in shining armor, he begins calling her Peaches to help her disassociate from the past of "Clarissa." A new name for a new start. Amos did exactly the same many years prior. On Earth, Amos was known as Timothy, but switched to "Amos Burton" when escaping for a new life in space. Now he wants Clarissa to have the same fresh start by washing away her old name and coming up with something new for the future.
While Amos is the one helping Clarissa currently in The Expanse season 5, it may not be long before their relationship becomes mutually beneficial. Amos has always been surrounded by unhealthy or platonic relationships - Lydia was a mother figure he may or may not have slept with, criminals forced him into sex work, and while Naomi remains a dear friend, there was never a romantic connection between them. In Clarissa, Amos might've found a partner who can help him take that final step toward becoming someone he can look at in the mirror.
