Sure, naming characters can help flesh out the world. But it is interesting that Monica is referenced by name so often when other, more significant background characters are not. Maya's dad, for example, has had a much larger impact on the story and even a brief appearance on screen, but no one has ever mentioned his name.
Personally, I think it's actually a side effect of Josy's characterization. She doesn't like or respect Monica, so she prefers to call her by name rather than the semi-honorific "my step-mom." We learn her name in the process more or less as collateral damage.
As for DPC's skills as a writer, I think you're a little hard on him. As I said above, he certainly has weaknesses, but he has very real strengths, too.