Again, please point to where she doesn’t know the St Patrick name. Nothing shows she doesn’t know that name as a public name, that scene wasn’t the connection of Riq to the St Patrick name either, it plays more into why he might be latching onto the family - knowing they can help his mom inside. Not sure what you’re watching but Monet clearly is suspicious of people, and Riq is the supreme suspicious dude - what people know of him on paper, he should be a square, but he’s shown he knows the game so she wants to know more about him...it’s that simple.
Because everybody on the show that knows Tariq knows of him as the son of the LT. Governor candidate who was murdered with his wife on trial for his murder. Monet seems to know nothing of it or hasn't mentioned it at all. Now maybe that's an oversight on the shows part or maybe she just doesn't know of the name.