Here we are 4.5 years since I found this reported and it's still a bug. 

Here's a breakdown of my workflow:
Name my artboards in the artboard palette, and when I'm ready, I export those artboards in Export for Screens. 

The bug presents itself as:
a) The artboard name in the Export for Screens is not what I named my artboard in the palette. It's an artboard name from before my edit—even if that edit was entered 20-30 minutes ago.

b) The name in Export for Screens is correct, but the exported asset still has the name before my edit.

It appears that when entering an artboard name in the palett, it only sticks the landing 50% off the time.