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Nothing major.
It looks like part of your code (in red) is missing...read iname
[ $iname ] || output;
if [ $iname -gt $SIZE ] || [ $iname -lt 1 ]; then
echo "Choice is out of range"
...

You have to be careful not to enter a number that is out of range. (zero or greater than the size of the list)

I made a few changes to catch that error and another bug I discovered...
function...

An attempt to stay close to your original script...
#!/bin/sh

declare -A AGES # associative name/ages array
NAMES=($(cat names.data | sort -u)) # unique names array...

Here is something to get started, to chew on :p

#!/bin/bash
#
#
# Variables
#
declare -A AGE # Create an associative array
NAMES="Kim Lee Jack Sam Nick Smith" # List with names
#...

Might be an option if the OP's intentions were clear...

The use of numbers suggests you want to use a simple vector array, but why not skip the numbers and use just names and an associative array?

I don't think above code is working fine. Having corrected several logical and syntactical errors, I'm still not sure I understand what you are doing - you have a list of six name constants, and six...

That's because the second time you (recursively) call function one, the else branch of if [ "$name" == "Sam" ]; will be taken.

BTW, you have a 16 bit char (0x 3000000, UTF8: 0xE3 0x80 0x80) in...

#!/bin/sh

function one ()
{
echo "Who is here"
read name
echo "Who old are you $name"
read age

[[ "$name" == "Sam" ]] && Sam=$age
[[ "$name" == "Jack"...