I don't really have a problem with the names, it's appropriate localization with just cause, not
stupid localization like changing a character name from "Itsuki" to "Iggy" or "Kyoichi" to "Kyle" (this
really happened).
I looked a little into it. As the chapter already said, the name Eliza comes from the Queen Elizabeth II Cup. Though contrary to what you said in the front page comments, I think the other girls' names also come from horse racing cup events, not individual race horses.
Again, I do like the names, they're well-done. I literally know someone called "Cherry". I like "Chrys" the most, it's a clever combination of a simple name, yet having had chrysanthemum tea before and knowing it's really sweet, it adds another layer, a warm feeling to the name. It wouldn't evoke that feeling if the name remained "Kikka". That's a pro of localization, it makes it more relatable to the target audience.
(Though personally I would have left it as Ouka, Shuuka, Kikka, as it saves me the headache of dealing with localization. But that's because I'm lazy. If you're willing to take the responsibility for the names of these girls, almost like the main character in the series, poetically, then by all means, go ahead.)