Running a stepper motor at under its rated current will affect both its maximum speed and torque (both holding and dynamic), though depending on the driver type, it mostly effects the torque.
Firstly, The stepper motor driver you are linking requires power rails of 7-30V. Its logic interface is 5 or 3.3v.
Furthermore, your stepper motor is 3.6 ohms per winding, so even with 3.3V rails, your motors are going to pull ~900 ma, which will cause power rail brownouts.
Fortunately, in this context, the stepper motor controller IC provides chopped current limiting, which is a technique which limits the maximum amount of current it runs through the stepper motor. Therefore, you can run the stepper motor you have off the wall-wart you have, a the cost of reduced torque.
In a system which uses current chopping, the voltage largely determines the motors maximum speed, and the current the torque. There is interactions, but they are fairly small in effect size (assuming you are not at extremely low voltage or current), proportionate to the effect of changing the relevant characteristic directly.
I urge you to carefully study the A3967 datasheet (the A3967 is the stepper motor IC the linked driver uses).
Furthermore, the designer of that stepper motor driver provides a fairly decent introduction into the concepts of how the device works here, which, from your question, I don't think you have really read. You should carefully read it before you hook anything up, lest you damage one of your parts.
Additionally, the stepper motor driver you link already has a voltage regulator, so you do not even need the voltage regulator you included in your post (SFE sku: PRT-00114).
See the schematic for the Stepper Driver Here. The voltage regulator is IC2.
At 12 V the speed will soon be zero since something will overheat and break. That's if this A4988 thing can even supply the necessary 7.5 A per phase. If not, then it will probably get hot and break. Either way, this is not a good idea.
There is one exception to this, which is if the 12 V is only applied for short periods of time to overcome the inductance of the windings, with the voltage then quickly brought back down to spec before the current exceeds spec. That sort of drive can be useful for steppers because the current in the coils switches faster, which allows the motor to run faster. However, care must be taken to not exceed the rated current. Unless this A4988 thing is specifically designed to do this and you can set a current limit at the 1.78 A maximum the motor is rated at, the points in the first paragraph apply.
Best Answer
You need the motor torque constant. It's sometimes called Kt and/or Ke. This parameter will let you relate current to torque. Then you can work backwards, starting with the torque you want, figure out what the current must be, and then ohms law will tell you what voltage will push that current.