No, it is not possible. From the docs, json-schema: …a JSON based format for defining the structure of JSON data.
It is quite limited for making data values validation because it is not the purpose of the standard. Many people have asked this before because it is common to request a kind of “unique Id” feature. Unfortunately for those who need it, json-schema does not provides you with that.
So if you want to ensure uniqueness your only option is to have “name” as property keys instead of property values.