Coming from the era where Friday night card parties/family get togethers/funerals/wedding receptions were (and, still are in many communities) held at the church hall, and the dishes of choice were those always present and wonderfully washable/reusable 'snack sets' that you'll now find in thrift shops/antique malls/or, my kitchen cupboard, I've always known this size as a luncheon plate. And, if I called it anything else, my mother would correct me - politely, of course!
Not to be confused with a dinner plate - the smaller 'luncheon' plate was used for the afternoon tea or coffee and ladies' luncheons, because it wasn't for a full meal, but rather for the afternoon 'break' or special occasions with maybe a cookie or two, a slice of Aunt Mary's awarding winning Red Velvet Cake - or, those little tea sandwiches.
There now, aren't you glad I added this silly little bit of trivia?
Carry on!