**It will depend on the context.** 

* I recall the term ["clamping" being used.](https://en.wikipedia.org/wiki/Clamping_(graphics))    It appears in various disciplines including numerical optimization and computer graphics.

* In the computer graphics area this is needed to distinguish it from an important, ubiquitous, but different operation called ["clipping"](https://en.wikipedia.org/wiki/Clipping_(computer_graphics)) 

* Despite that, ["clipping" is used in signal processing](https://en.wikipedia.org/wiki/Clipping_(signal_processing)) to denote your operation.

* There is a closely allied operation in statistics called ["Winsorizing"](https://en.wikipedia.org/wiki/Winsorizing).  Winsorizing can be construed as beginning with a data-dependent clipping operation.

[![Graph][1]][1]

This graph of the "clipping" or "clamping" operation was created by plotting the function $x \to a \vee (b\wedge x)$ (where $\vee$ is the maximum and $\wedge$ is the minimum).  It visually demonstrates that

1. Clipping is piecewise linear.

2. It can be construed as a special form of linear ["spline"](https://gerardnico.com/data_mining/linear_spline) connecting the points $(a,a)$ and $(b,b).$  (Applying affine transformations to either or both coordinate will transform it into a linear spline between any pair of distinct points.)  See https://stats.stackexchange.com/a/291598/919 for the theory and code.


  [1]: https://i.sstatic.net/uOeFE.png