Imaginary numbers are not pairs. Complex numbers are. Continuing Gauss, I'd rename "complex numbers" as "planar numbers".
Also vector numbers could be somewhat of a useful name, since they behave like a 2D vector (or even higher dimensional vectors for e.g. quaternions)
Don't know how relevant this is, but I've been thinking about a better naming scheme for hypercomplex number systems. I came to it after seeing a paper about the "dual-complex numbers", which are not a straightforward complexification of the dual numbers as one might expect. Hopefully, the scheme should be pronounceable, and without the possibility of confusing it for something else. This town needs law! I'm thinking of asking for suggestions for what it should be exactly.