The name paravector is used for the sum of a scalar and a vector in any Clifford algebra (Clifford algebra is also known as geometric algebra in the physics community.)
This name was given by J. G. Maks, Doctoral Dissertation, Technische Universiteit Delft (Netherlands), 1989.
The complete algebra of paravectors along with corresponding higher grade generalizations, all in the context of the Euclidean space of three dimensions, is an alternative approach to the spacetime algebra (STA) introduced by David Hestenes. This alternative algebra is called algebra of physical space (APS).
Read more about Paravector: Fundamental Axiom, The Three-dimensional Euclidean Space, Higher Dimensions, Matrix Representation, Lie Algebras