Sigma protocol with Pedersen commitment and Hash function
This is no longer a secure commitment. Note that there should not be any way to efficiently verify if a given commitment value $c$ is to a message $m$. However, once you derive the randomness in this way, an attacker could try to guess $m$ and verify if this guess is correct by checking if $g^m\cdot h^{H(m)} = c$. Thus, this is not a secure commitment scheme.