It's fine wiring the two circuits in parallel from a 12V supply. I'd probably put a zero ohm link in series with each group in case one went badly wrong - I could then take the link out and see that one was still working and the other was broken. Maybe even consider a small resistor so you can measure the two individual currents to both circuits - something like 0.1 ohms.
On the negative side, the L298 isn't very good for this sort of thing - it will drop (on each transistor) about 1.3V at 1A and if your stepper motor coil needs the full-juice from the 12V, be prepared to be disappointed with results. However, if you only need (say) 250mA to drive the coils then it should be OK. Here's the data anyway: -
What this means is that from a 12V supply the stepper motor coil will not see 12V but something more like 9.4V at 1A load. If this is a continual drive the chip will dissipate 2.6W per channel.
There are better chips around that use MOSFETs and drop a fraction of the voltage.
EDIT - added info on a better chip
The DRV8841 is a better choice for what I believe you might need. It's dual H bridge therefore will drive one stepper motor and works from over 8 volts up to over 40. It's got PWM circuits that can regulate the current too (that can of course be disabled). The on resistance of each transistor is typically 0.25 ohms at 1A - a full H bridge would dissipate 0.5 watts and you'd lose 250mV per transistor meaning that instead of about 9.5V being applied to the coil, it's be more like 11.5 volt. Also, because the power transistors are FETs, the parasitic diode in nearly all FETs, saves you having to uses the external diodes in your circuit.