Regulate high current LED light with potentiometer (voltage regulator or voltage divider)
My goal is to regulated voltage to these LEDs to be from 2 V to 3.4 V (or 0 V to 3.4V if not possible to limit the low voltage) and constant current of 3A.

It doesn't work that way.  You can regulate current or voltage, but the load decides what the other is.

In any case, what you want to do here is regulate current.  The LED voltages then come out to whatever the LEDs decide, based on lot variation, temperature, age, and other factors.

Since you want to regulate current and have that be the same thru each LED, you should connect them in series, not parallel.  So now you need a 1 A current supply that can output from 8.25 to 10.2 V.

Since the battery voltage is reliably lower than the lowest voltage you need to put out, you need a boost converter.  Use a small low side current sense resistor to measure the current thru the LED string, then control the switcher to regulate the current to 1 A.  For example, a 100 m&Omega; resistor will drop 100 mV at 1 A.  That's enough to comfortably gain up to drive the A/D input of a microcontroller.  However, it only dissipates 100 mW, which is a small fraction of the 8.3 W minimum going into the LEDs.

For dimming, connect the pot as a separate input to the microcontroller.  The boost switcher control algorithm takes this input into account in deciding what the desired LED current should be.  This has another advantage that the current doesn't have to be a linear function of the pot setting.  Humans perceive light level logarithmically.  You want a fixed rotation of the pot to cause a fixed ratio of current change.  This can easily be done with a lookup table or simple formula run on the pot reading.  Note that this can be done in foreground code and can be "slow" since it only has to respond in human time.

Using more batteries

You have now asked about using additional cells in series to avoid using a boost converter.

Yes, you can use multiple cells in series.  Enough cells in series increases the voltage so that it wouldn't need to be raised, only dropped.  Now you need a buck converter instead of a boost converter.  The relative complexity of these two is similar, although a booster will be a little easier in this case (low side switch and low side current sense).

The worst case is when the battery voltage range and the LED voltage range overlaps.  Then you sometimes need to increase the voltage, sometimes decrease it.  That is more complex than always increasing it (boost converter), or always decreasing it (buck converter).  I would stay away from this regime since it adds complexity and can be fairly easily avoided in this case.

Multiple cells in series present the additional problem of balancing during charging and detecting the lowest voltage of any cell while discharging.  The latter is required to shut down to avoid cell damage.

You seem to be asking about how to use a pot directly in-line with the LEDs somehow to perform dimming, and seem to be wanting to use a linear regulator.  Both these are a bad idea.  This is a battery operated device, so presumably power efficiency is important.  Both a pot in series with the LEDs or a linear regulator would dissipate significant power.  Not only does that waste energy from the limited amount stored in the battery, but now you also have to get rid of the heat caused by that wasted power.  A boost or buck converter will be smaller, cheaper, and lighter than something less efficient after considering the extra mechanisms for dealing with the heat.