This recipe is called Date Sandwich Cake in some old cookbooks. Other variations are Raisin Squares or Fig Squares.
Date Squares (Matrimonial Cake, if you happen to come from the West) are a real nostalgia treat. The fillings in the 30s recipes were extremely sweet. Today’s versions reduce the sugar in the filling, since the dates are sweet enough, and are often microwaved.
Raisin Puff, an old favorite in P.E.I., is somewhat similar, with raisin filling sandwiched between layers of soft cookie dough instead of an oatmeal mixture.