Red Haired Girl In The Bed With Pillows

The opening/closure of pillow cases ranges from the straightforward approach in USA called simply 'bagstyle' to the more usual European method with a pocket inside the open end to fully contain the pillow. This is Housewife style.
"Housewife is ...essentially a bag, with a flap in the open end to tuck the pillowcase behind to keep it in..."
Other methods of closure are ties or buttons/buttonholes.