This procedure doesn't conform to any particular calling convention. It is designed specifically to work with other subroutines designed by me. Any of my examples won't be using and standard library functions either. Not because I think they are inadequate, but rather give me complete independence and easier porting I think to an OS less app relying only on BIOS functions.

The purpose behind this design was to facilitate a very tight loop involving multiple NULL terminated strings

 Array  db  'One', 0, 'Two', 0, 'Three', 0, 'Four', 0, 0
 Prompt db  ' times', 10, 0

        mov     esi, Array

    L0  call    Show
        push    rsi
        mov     esi, Prompt
        call    Show
        pop     rsi
        cmp     byte [rsi], 0
        jnz     L0

I think you can see the result would be

One times
Two times
Three times
Four times

In any event, it makes for a pretty low overhead loop.

Display a null terminated string on monitor or to whever stream is directed.

    ENTER:  RSI = Pointer to null terminated ASCII string.

    LEAVE:  RAX = Character count including NULL (terminator)
        RSI = Next string (if it exists). 

   0:   57                      push   rdi
   1:   52                      push   rdx      Preserve
   2:   51                      push   rcx

    Determine strings length. 

   3:   48 83 c9 ff             or     rcx, -1      Should be large enough
   7:   31 c0                   xor    eax, eax     Need all bits cleared @ 16 anyway
   9:   56                      push   rsi
   a:   5f                      pop    rdi      Source buffer
   b:   f2 ae                   repnz scasb     Find terminator hopefully
   d:   48 f7 d9                neg    rcx
  10:   83 e9 02                sub    ecx, 0x2

  13:   57                      push   rdi      Need this again @ 1C

    Now we can setup for system call.
        RDI = STDOUT
        RSI = Pointer to string
        RDX = Number of characters to display

  14:   51                      push   rcx
  15:   5a                      pop    rdx
  16:   b0 01                   mov    al, 0x1
  18:   50                      push   rax
  19:   5f                      pop    rdi
  1a:   0f 05                   syscall

    I don't think it's really necessary to check for errors here as operator will 
    probably be aware without prompting.

  1c:   5e                      pop    rsi      Next string possibly

  1d:   59                      pop    rcx
  1e:   5a                      pop    rdx      Retrive
  1f:   5f                      pop    rdi

  20:   48 ff c0                inc    rax      Bump to include terminator
  23:   c3                      ret