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 baseball roster is to help keep the team organized. The B stands for the word bat and helps to keep track if the player bats from the right or the left side. The letter T stand for throws and whether they throw left handed or right handed. There is also the letter S, which stands for Switch Hitter.
Bats / Throws Which hand/side the player uses when he bats, and what hand he throws with.
MLB player Curtis Granderson throws right.
MLB player Brian McCann throws right.
MLB player Brock Holt bats left.
Will Smalley bats right and throws right.
Will Sawyer bats left and throws left.
MLB player Kevin Kiermaier bats 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.