You call him bats-left-throws-right. That's not very unusual at all. The other way around, however, is highly unusual. The only player who comes immediately to mind is Ricky Henderson. He was a southpaw who batted right. Strange, indeed.
The "B" stands for bats, whether the player hits from the right side or left side or is a switch hitter (S) The "T" stands for throws, whether the player throws righthanded or lefthanded.
Bats / Throws Which hand/side the player uses when he bats, and what hand he throws with.
Will Smalley bats right and throws right.
Will Sawyer bats left and throws left.
Ollie Smith bats left and throws left.
Bill Snyder bats right and throws right.
Bill Sullivan bats right and throws right.
Harry Sullivan bats left and throws left.
Marty Sullivan bats right and throws right.
Fred Walden bats right and throws right.
Deke White bats left and throws left.
Art Williams bats left and throws right.