For a sine wave $x=A\sin(ωt+\varphi)$,
- $A$ is the amplitude
- $\omega$ is the frequency
- $\varphi$ is the phase
What is $(ωt+\varphi)$ called? "Angle"? I can't find any source call that part.
$\omega t + \varphi$ is called the phase. See this Wikipedia article for the details.
The symbol $\varphi$ is known variously as the phase shift, phase offset or phase constant.
As with functions in general, the quantity inside $\sin$ here is called an argument.