You had several issues. I've made some changes that should work. This leverages the Jamf binary to change the name rather than scutil of which your syntax was wrong anyways.

One thing you'll need to do is set your $MAC variable. I'm not sure what that is even doing. Also, you may consider setting up something so that if somebody chooses "New York" as the location then in the computer name it only puts "NY" etc. so that you don't have that long of a computer name.

#!/bin/bash

# Set CocoaDialog Location
CD="/Users/Shared/CocoaDialog.app/Contents/MacOS/CocoaDialog"
last7ofserial=$(system_profiler SPHardwareDataType | awk '/Serial/ {print $4}' | rev | cut -c -7 | rev)
mac="$MAC" # This is definitely an issue. You have not set the $MAC variable so what is this even doing?
errorIcon="/System/Library/CoreServices/CoreTypes.bundle/Contents/Resources/AlertStopIcon.icns"

# Dialog to enter the Location and the create computerName variable
while [[ -z "$location" ]]; do
    location=$("$CD" standard-dropdown --string-output --title "Choose a Location" --height 150 --text "Please choose a location." --items "London" "New York" "Shanghai")
    buttonClicked=$(/bin/echo "$location" | awk 'NR==1{print}')
    # Below will prompt for location, print it to upper case, then remove spaces
    location=$(/bin/echo "$location" | awk 'NR>1{print}' | awk '{print toupper($0)}' | sed 's/ //g')
    [[ $buttonClicked = "Cancel" ]] && echo "User canceled; exiting." && exit 0
done

while [[ -z "$deviceType" ]]; do
    deviceType=$("$CD" standard-dropdown --string-output --title "Choose a Device Type" --height 150 --text "Please chose a device type." --items "LT" "DT")
    buttonClicked=$(/bin/echo "$deviceType" | awk 'NR==1{print}')
    deviceType=$(/bin/echo "$deviceType" | awk 'NR>1{print}')
    [[ $buttonClicked = "Cancel" ]] && echo "User canceled; exiting." && exit 0
done

computerName="${location}${deviceType}${mac}${last7ofserial}"

# Use Jamf Binary to set Hostname using variable created above
/usr/local/bin/jamf setComputerName -name "$computerName"

# Dialog to confirm that the hostname was changed and what it was changed to.
if [[ "$?" == "0" ]]; then
    $CD ok-msgbox --text "Computer Name Changed!" 
        --informative-text "The computer name has been changed to $computerName." 
        --no-newline --float --no-cancel &> /dev/null &
else
    $CD ok-msgbox --text "Error!" 
        --informative-text "There was an error changing the computer name." 
        --icon-file "$errorIcon" --no-newline --float --no-cancel &> /dev/null &
fi

exit 0

@jthurwood Does that help?