I'm just using this script to collect the connected display at the time of an inventory collection, the caveat its works fine if you have a static environment but obviously in Agile, where users roam around and connect to different displays it may not suit your needs

!/bin/sh

displays=$(system_profiler SPDisplaysDataType -xml | grep -A2 "</data>" | awk -F'>|<' '/_name/{getline; print $3}')
echo "<result>$displays</result>"

@gbidwell Thanks, that's great!

Do you have a method of collating the data after the script is run?

We use the script as a EA (Extended Attribute), then we just add it to admins standard inventory display then it shown in every smart/static group window created as default.
The results are then just exported as required depending on what we need to audit at the time

As the EA is reliant on getting the data on the inventory collection process it took a week or so before all computers naturally checked in and updated this field with a result.
Others may have a better way of doing this, but the above EA served our requirement.