You seem a little confused about battery requirements (that's not meant as a criticism - confused is the standard place to start!)
Your battery is at 4.2 volts when it's fully charged. As it discharges it drops to about 3.2 volts, at which point your mod will tell you that it's low and refuse to fire.
There's also the voltage that your coil gets, which isn't the same as the battery's voltage. That's the voltage your mod probably shows. With a regulated mod, it isn't a particularly important value.
If your battery is at 3.4 volts, for example, and your wattage setting means the coil needs 3.7 volts, then your mod will simply pull more current from the battery and use it to 'bump' the voltage up to 3.7 volts at the coil.
The things you need to know to make sure you're using a battery reasonably safely in a regulated mod are:
- Battery CDR (continuous discharge rating) - the best way to work this out is to check your battery model against Mooch's tables. You say you have a Murata, but do you know which model it is? VTC6 is probably the most common, but others are often used as well.
- The wattage you're vaping at
- The number of batteries in your mod
If you're interested in seeing the calculation for your setup, try to find out your battery model and I'll show you how it goes.
Good luck!