It has been shown that a variety of names are assigned to the original MHD Alfven wave derived originally by Hannes Alfven in the 40s (Nature 150, 405-406 (1942)), and those names are used due to the different magnetic geometries where the target plasma could be confined, that is, in laboratory, in fusion, in space, and in astrophysics, where one could use as working geometry systems such as cartesian, cylindrical, toroidal, dipolar, and even more complex ones. We also show that different names with no new dramatic new physics induce misleading information on what is new and relevant and what is old related to the considered wave mode. We also show that changing the confining geometry and the background plasma kinetic properties, the Alfven wave dispersion properties change accordingly and this change “induces” all types of non-necessary swarm of names for the same MHD shear Alfven wave derived previously by Alfven.