What makes a stepper motor run faster?
Your problem is the Arduino. I assume that you connected a digital pin to the STEP of your motor driver. There is an upper limit for the frequency (see AccelStepper Doucmentation), which is around 1000 pps (points per second). Assuming that you have a standard stepper with approx. 200 steps / revolution this would only result in 300 rpm (rounds per minute). For many applications this is too slowly.

So how can you go faster? I would recommend to use a "PWM chip" as a controller and connect that one to the STEP of your driver. With that you have sort of a speed control. I am currently searching for an appropriate PWM chip, if I find something, I will update this answer. Perhaps some small chip which does "i2c to pwm with variable frequency". I know that Adafruit did something like that but they only achieve 1.6 kHz.