Could you update that last sentence in your question? I'm not quite following.
I have had plenty of tables that had no need of a sort key so that can be left out. All tables must have at least 1 partition key (primary key). That's the only index that you can query on. If you need more than one you can add a global secondary index (GSI) and you can query on that.
So if you table were to look like this
[PK, SK, name, date, ...]
I can now query on PK (partition key) and filter by SK (sort key). I cannot query by name, date or whatever else is in the table.
However if you table was structured like this
[PK, SK, name(GSI), date, ...]
I can now query by the global secondary index name as well. https://docs.aws.amazon.com/amazondynamodb/latest/APIReference/API_Query.html
So I think the answer is no. Your partition keys must be unique. If you attempt to add the same one again it will fail unless you're use the update method which will update the existing item if it exists or create a new item if it does not.
Edit: Although my answer isn't strictly wrong the actual key of the item in the database is based on the combination of the PK and SK. So you could have multiple items with the primary key of Iowa and a secondary key of 123 456 or 789 and in your query you must include both the PK and SK to get the exact item you're looking for.
[
IOWA (PK), 123 (SK),...,
IOWA (PK), 456 (SK),...,
]
https://aws.amazon.com/blogs/database/choosing-the-right-dynamodb-partition-key/