Yes, in the Z80 BC was a sort of counter register (e.g. for LDIR or DJNZ instructions), which is perhaps why BC became CX. In the 8080 there wasn't much difference between BC and DE.
The interesting part is that BX maps to HL, which explains the weird order AX/CX/DX/BX in the encoding of 8086 instructions.
The interesting part is that BX maps to HL, which explains the weird order AX/CX/DX/BX in the encoding of 8086 instructions.