section .data

prompt      db  "Please enter your name: ", 10
length      equ $ - prompt
text        times 255 db 0
buffer      times 255 db 0

Enter your text
section .text
global main
main:
    mov  rax, 1
    mov  rdi, 1
    mov  rsi, prompt
    mov  rdx, length
    syscall

    mov  rax, 0
    mov  rdi, 0
    mov  rsi, text
    syscall

    mov  rcx, rax  ; rcx will be the character counter.
    mov  rsi, text ; a pointer to the current character. Start from the beginning.
    add  rsi, rcx
    dec  rsi       ; Remember the 0-index
    mov  rdi, buffer

;; This subroutine is also SUB-optimal if your teacher demands
;; performance, look into the advantages of `lea` and a simple
;; rep;scas loop as well.
process_loop:
    mov bl, [rsi]               ; Now copy from back to front
    mov [rdi], bl
    inc rdi
    dec rsi
    dec rax
    jnz process_loop

    mov  rax, 1                 ; And print the string
      mov  rdi, 1
      mov  rsi, buffer
      mov  rdx, rcx
      syscall

exit:
    mov     rax, 60
    mov     rdi, 0
    syscall