Why is q used for specific humidity?
The specific humidity q is a quotient - mass of water vapor in mass of moist air. The mass is expressed per volume, i.e. the density of water vapor $\rho_v$ and the density of dry air $\rho_d$ are used for the definition of the quotient $q$ known as specific humidity:

$$ q = \dfrac{\rho_v}{\rho_v+\rho_d} $$