People just called them mudholes around here. A good place to bury a tractor. Or a pickup. I remember when we were hunting back in the 60s one guy drove out into the middle of a playa and got stuck. We had to borrow about 300' of chain from nearby farms to pull him out!
Calling them playas isn't merely a matter of style, it's the generally accepted term used by both science and government in referring to ephmeral wetlands of the Great Plains. I'm not sure when the USDA and USFWS and other agencies started using the term 'playa', but these days it appears in the title of many studies like this one:
There must have been a push to use 'playa' in government documents about 25 years ago, at least when I first saw it gaining prominence in the soil conservation business. I'm sure someone reading this knows even more.