I think you're looking for "overpowering the ambient light", or, more graphically, "killing the ambient".
This means using artificial lighting so bright that it outshines the regular sources, usually the sun. (Dim indoor lighting is easy enough to overpower that it's scarcely talked about, but if you really want absolute control of the light, should be considered too.)
There's a little bit of nuance to it. Stopping down the aperture (or lowering ISO) reduces ambient light and flash together, so you need faster shutter speed.
Shutter speed is limited by two things: first, your camera's shutter sync speed, and second, the duration of the flash pulse itself. The former is usually something around ¹⁄₁₈₀th to ¹⁄₂₅₀th of a second. The flash impulse itself is something we think of as very fast, but actually at full power a speedlight-style hotshoe flash can be as slow as ¹⁄₁₂₅th when you measure the T.1 duration — the time in which the flash pulse at least 10% of the peak. (Flash duration is often given as T.5 times, which are effectively the same for speedlights at fractional power.)
A leaf shutter (rather than a focal plane shutter) or an electronic shutter can provide a faster sync speed, which can help, but that's usually not an option with the equipment you probably have (or want to spend for).
So, that means you really just need a powerful flash, and there's no tricks to get around it. "High speed sync" doesn't really help, because that's effectively continuous light and therefore also reduced by shorter shutter. Multiple flash units can do it (whether in HSS mode or just to provide more light), and it helps to get your light as close as possible because of our friend the inverse square law.