In mathematics, a projection is a mapping of a set (or other mathematical structure) into a subset (or sub-structure), which is equal to its square for mapping composition (or, in other words, which is idempotent). The restriction to a subspace of a projection is also called a projection, even if the idempotence property is lost.
Is there a specific term for an analogous mapping from one space to a higher dimensional space?
Unprojection!
For an example of this usage, see: https://dondi.lmu.build/share/cg/unproject-explained.pdf