Why is the dimensions of pressure head equal to the dimensions of length when pressure head is pressure per unit volume?

No pressure head is not pressure per unit volume. It is defined as follows

ψ=pγψ=pγRefer above for definition of p and γNewtonMLT-2PressureML-1T-2ψ=ML-1T-2ML-1T-2L-3ψ=ML-1T-2ML-2T-2ψ=M1-1L-1--2T-2--2ψ=M0L1T0

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