Why BLDC are DC motors as basically they work on ac by using inverter? Can I directly give AC supply to BLDC motor?
BLDC motors, or brushless Direct current motors, are, as the name suggests, motors which have no brushes and are powered from DC.

You are correct, they use a style of inverter to convert from DC to a waveform which switches to activate the windings of the motor as required. However, this is not an AC motor, as an AC motor is tuned to operate at a speed to use the fluctuations of the supplied AC. The BLDC unit is designed to operate from DC which is switched as required by the motor. AC motors tend to be large, steady state, single speed style of motors powered by mains electricity. BLDCs are a lot better at handling different speeds (in very general terms).

An AC motor is defined from the AC supply. The "inverter" of the DC motor is defined from the motor.