What's the name of data points that trained model gets on input in production? I need some machine learning vocabulary advice.

What do you call input data that a trained model gets in production?

I know that labelled or unlabelled data it gets during training is called training set or training data. 

When it's ready, after initial training, you deploy it in production to solve real problems. How do you call the input data that the model receives at that point?
I think you're talking about production data.  This is typically real data that you generate or acquire somehow, and it's the data you expect your trained model to classify or use to make predictions.  

You mention that this is after initial training.  I'm assuming you've already used test data to measure your model's accuracy, and this is in fact now in production.