Can I keep half of an addressable led strip on?
If you have the two strings of 150 LEDs you would be controlling them individually so the choice of which set is on or off is obvious.

If the string of all 300 LEDs is all in one string then your control system needs to deal with sending out the serial command strings for the 300 daisy chained LEDs. In this data stream you would set the off state controls for those LEDs that you want off and those that you want to have ON. It could be any mix that you want and would not be limited to the first or last 150 in the string.

This level of control does imply that you have a microcontroller based control system that you program to achieve the on/off/color pattern that you want for each of the 300 LEDs.