The X means pair, and goes back to at least the 8080. It had 8-bit registers B,C,D,E,H,L (among others) which could also be used in pairs (BC, DE and HL). The BC and DE pairs were used mostly for 16-bit arithmetic; the HL pair generally held a memory address. Some examples of the usage of X for pair:
LXI D,12ABH ; "load pair immediate"
DCX B ; "decrement pair"
STAX D ; "store A (indirect) at pair"
Fast forward to the 8086. It has registers AL,AH,BL,BH,CL,CH,DL,DH, which, similarly to the 8080, can be used in pairs: AX, BX, CX, DX.
As others have pointed out, the E in the 32-bit register names means extended.
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