No, you weirdos. We're joking. Arrowsmith came out in 1925 and Steven Tyler's luscious lips didn't start making beautiful music until 1970.
Arrowsmith is in many ways a fictional biography, so it makes sense that the title would be the main character's name. But on top of that, Martin's name is also symbolic in its own right. Martin has a commitment to scientific truth that makes him wish that he could fly as straight as an arrow through life, never swerving from the path of pursuing scientific Truth.
The problem is that (life lesson, kids) the world is a complicated place and filled with people who always try to steer Martin off course by offering him money and power. By the end of the book, it looks like Martin has finally gotten onto the track he's always believed in. The problem is that he has left some death and destruction in his wake.
But death and destruction is sort of an arrow's job, come to think of it.