Lenses are specified by their focal-length or focal-range for a zoom with the focus set to infinity (unless it cannot, which is possible). Given your example, a 16-50mm has a 16mm focal-length at its widest position and a 50mm focal-length when most zoomed in. Again, this measurement is taken at infinity, so the focal-length can be slightly different with when focused closer.
A 16-50mm lens is labelled 16-50mm because that is its focal-length. A lens gives a different field-of-view on a full-frame than on a cropped-sensor camera, This is what the Crop-Factor or Focal-Length-Multiplier refers too. With an FLM of 1.5, a 16-50mm lens gives the same field-of-view as a 24-75mm lens on a full-frame. Now if you had a 24-75mm lens compatible with a full-frame camera, it would give the same field-of-view on that camera but if you mounted it on an APS-C camera, it would show the equivalent of 36-112mm lens.
Where you will see lenses labelled as their effective focal-length is on fixed lens cameras since there you have no choice and point-of-reference to determine what field-of-view is obtained. The exception to this rule is the Pentax Q system which originally specified their lenses in terms of effective range but then had start specifying 2 sets of focal-lengths or focal-ranges when they increased the sensor size from 1/2.3" to 1/1.7" starting at the Q7.