how to tell if a recent Wassily chair is real?  

I assume that contacting...
I assume that contacting Knoll would provide requested info.
To my knowledge, in the U.S. Knoll has been stamping the chairs for the last several years (how long I do not know).

Gavina
I have a pair of heavy Wassily chairs that were in my brother's Olivetti dealership in the 70s. They have a foil label on the back or the seat frame that says "Gavina" and numbered 7333. Label also shows "Wassily" and "Knoll". I guess this means that Gavina commissioned the chair design to be sold. Don't know for sure
From Ask.com:
The origins of this Italian furniture-manufacturing firm lay in Bologna, where Dina Gavina began furniture production in 1949, although the company was not formally established until 1960. Gavina sought to explore a more artistically charged yet contemporary aesthetic that provided an alternative to the functional aspects of Rationalism, the progressive language of the Italian avant-garde in the interwar years. Notable designs commissioned by Gavina included the lyrical, flowing form of Achille and Piergiacomo Castiglione's Sanluca chair (1960), Marco Zanuso's Lamda chair (1963), and Afra and Tobia Scarpa's Bastiano sofa (1961, later produced by Knoll International). In 1962 the company also attracted favourable attention through its reproduction of the 1920s classic tubular steel furniture by the Bauhaus teacher Marcel Breuer. Gavina was well connected in the Italian design world and played an influential role in its development and was a co-founder with Cesare Cassina of the innovative Italian lighting manufacturer Flos. In 1968 Gavina sold his company to Knoll International.