Usually after the device was accepted you will see something in the logs of mender-client, that the client is updating the inventory. While the mender-client is running you can add inventory on the fly. Maybe consider using --demo-polling so the time intervals are short.
mender setup \
--device-type $DEVICE_TYPE \
--server-url https://eu.hosted.mender.io \
--tenant-token $TENANT_TOKEN \
--demo-polling \
--server-cert /etc/mender/server.crt \
--data /var/lib/mender
You could add a custom script that will be automatically evaluated by the client and update the info.
/usr/share/mender/inventory/mender-inventory-<my_custom_script>
With contents like
echo "device_type=$DEVICE_TYPE"
Take a look at already present scripts