The L293D can be connected to a 5V power supply like from an Arduino at pins 1, 8, 9, 16. Now if I need more power for the motors I supply let's say 9V to the pin 8 separately. My question is, if the IC uses like 1.5V from which power supply will the voltage drop? The one where I supply the 5V (pins 1, 9, 16) or the 9V supply (pin 8 )?
You need +5 at pin 16 for Logic Power (VCC1).
You supply a high signal at pins 1 and 9 to enable the output drivers.
You supply motor power at pin 8 (Vcc2).
Any power supply drop will then be seen from pin 8 to the Y output pins 3,6,11,14.
This is documented on page 5, electrical characteristics VOH and VOL.
Never let the motor voltage drop below the logic supply, or you'll start taking current from that via
internal circuitry (AFAICT this is a design flaw in the chip).