The 4 refers to the 'Active Four' which is 4WD, 4WS, 4ABS and 4IS. You could probably add 4Valve into that too.
VR has been used as a model designation on the JDM 5th gen Galant turbo sedan (G63B SOHC 12V and FWD) so I guess it just makes sense VR-4 is a natural progression of the VR model. The VR badge did make a come back on the NZDM 8th gen Galant with the 6A13 V6.
For the JDM 6th gen Galant they came in a few 'series' - G, M and V with GF-4 being top of the G series, MX-4 being top of the M series and VR-4 being top of the V series. Likewise the 6G Eterna had a 'Z series' containing ZZ, ZX, ZX-4 and of course ZR-4 being the top of the Z series and top of the entire range.