CosmosDB SQL API: Change property Name - (Partial Updates .Net SDK or loops)

Yes you are right, Current version of Patch does not support patching nested array. You need to know the index in order to replace/add values as you mentioned in the first question.

One way to think about this would be to write your own logic to replace the keys , there are libraries available in dotnet and then using the bulk insert using the SDK to insert those documents.