2 layer are from different Arcgis Rest api endpoint URL, both can be label with ESRI label
https://transparentgov.net:3200/googlemaps7717/default?layer_id=1&layer=STVR_exempt_zone¢er_lat=33.692842624654844¢er_long=-116.27551396174243¢er_zoom=14&url=https%3A%2F%2Fgis.la-quinta.org%2Farcgis%2Frest%2Fservices%2Fshort_term_vacation_rentals%2FSTVR_exempt_zone%2FMapServer&org=La+Quinta+CA&overlayType=overlayType_image&panto=0&dynamicLabelField=name&url2=https%3A%2F%2Fgis.la-quinta.org%2Farcgis%2Frest%2Fservices%2Fshort_term_vacation_rentals%2FSTVR_exempt_zone%2FMapServer&layer_id2=3&dynamicLabelField2=Res_Comm
https://transparentgov.net/json2tree/esri/server/folder.html?url=https%3A%2F%2Fgis.la-quinta.org%2Farcgis%2Frest%2Fservices&org=La+Quinta+CA&_center_lat=33.6634&_center_long=-116.31&_center_zoom=17&select_folder=28&select_layer=1
Example 2
Riverside City layer and Riverside school district layer are different layers from 2 seperated Arcgis REST api endpoint URL.
This example you can label both of layer with ESRI label.
https://transparentgov.net:3200/googlemaps7717/default?layer_id=4&layer=Cities¢er_lat=33.86770043193115¢er_long=-116.24504296304787¢er_zoom=10&url=https%3A%2F%2Fgis.la-quinta.org%2Farcgis%2Frest%2Fservices%2Fcity_sphere_of_influence%2Fproposed_city_sphere_of_influence_extension%2FMapServer&org=La+Quinta+CA&overlayType=overlayType_image&dynamicLabelField=default&panto=0&select_folder=32&select_layer=6&url2=https%3A%2F%2Fgis.la-quinta.org%2Farcgis%2Frest%2Fservices%2FSchool_Districts%2Fschool_districts%2FMapServer&layer_id2=6&dynamicLabelField2=default
https://transparentgov.net/json2tree/esri/server/folder.html?url=https%3A%2F%2Fgis.la-quinta.org%2Farcgis%2Frest%2Fservices&org=La+Quinta+CA&_center_lat=33.6634&_center_long=-116.31&_center_zoom=17&select_folder=64&select_layer=4