The Cox proportional hazards model is sometimes called a semiparametric model by contrast.
The hypothesis of no change with time (stationarity) of the coefficient may then be tested.
Details and software (R package) are available in Martinussen and Scheike (2006). Perhaps as a result of this complication, such models are seldom seen.
The term Cox regression model (omitting proportional hazards) is sometimes used to describe the extension of the Cox model to include time-dependent factors.
However, this usage is potentially ambiguous since the Cox proportional hazards model can itself be described as a regression model.
In this case, the baseline hazard is replaced by a given function.