Potentiometer as Voltage regulator 12V to 6 - 12V range
What you are doing is not voltage regulation, but rather adjusting the resistance in series with the LEDs. This is a fine way to adjust brightness in principle - though it won't be linear, as you've observed - except for the fact that a potentiometer is not rated to carry the sort of current that flows through an LED strip. Potentiometers tend to be rated at 100mA or less, but 1.5 meters of LEDs will draw a lot more than that.

Your best option for controlling brightness fairly linearly is an adjustable constant-current supply - such as one like this:



An alternative that solves the power dissipation issue but not the linearity issue is to use a linear regulator like the LM317 with a potentiometer in the feedback loop - see that part's datasheet for an example.