Use serde_with and its #[serde(rename = "$key$")].

use serde_with::{serde_as, KeyValueMap};

#[derive(Serialize, Deserialize)]
struct Item {
    #[serde(rename = "$key$")]
    name: String,
    some_field: usize,
}

// This would be the enclosing type
#[serde_as]
#[derive(Serialize, Deserialize)]
struct MyMap(
    #[serde_as(as = "KeyValueMap<_>")]
    Vec<Item>,
);