What's wrong with "brifter"? It accurately describes the combination shifter/brake lever and avoids copyrighted marketing names like STI and Ergo.
BTW, there is another road "brifter" configuration, the Gevenalle version that uses downtube or barend levers mounted on modified brake levers. They are marketed primarily to cyclocross riders but are wonderful, versatile, durable brifters for road and touring bikes too.