Jelly, 12 bytes

⁵ṁX€’©+OỌ,®Y

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How it works

⁵ṁX€’©+OỌ,®Y  Main link. Argument: s (string)

⁵             Set the return value to 10.
 ṁ            Mold; create an array of 10's with the length of s.
  X€          Pseudo-randomly pick a integer between 1 and 10, for each 10.
    ’         Decrement, so the integers fall in the range [0, ..., 9].
     ©        Copy the result to the register.
      +O      Add the integers to the ordinals (code points) of s.
        Ọ     Unordinal; convert back to characters.
         ,®   Pair the result with the key.
           Y  Join, separating by a linefeed.