#!/usr/bin/env bash

list=("fname" "lname" "phone" "dob")
args=()  # an array for args will be safer
for f in "${list[@]}"; do
  read -p "${f}: " a
  args+=(--arg "$f" "$a")
done
jq -n "${args[@]}" '$ARGS.named'  # no need for potentially dangerous 'eval' now