The JSON spec says this:
An object is an unordered set of name/value pairs.
The important part here is "unordered": it implies uniqueness of keys, because the only thing you can use to refer to a specific pair is its key.
In addition, most JSON libs will deserialize JSON objects to hash maps/dictionaries, where keys are guaranteed unique. What happens when you deserialize a JSON object with duplicate keys depends on the library: in most cases, you'll either get an error, or only the last value for each duplicate key will be taken into account.
For example, in Python, json.loads('{"a": 1, "a": 2}')
returns {"a": 2}
.