With map services in Portal and AGOL I am able to label features using attributes. For my project I was using the ESRI USA roads service. https://landscape1.arcgis.com/arcgis/rest/services/USA_Roads/MapServer
When I brought the same service into Pro as a service, there were no label options. This seems to be an oversight and should be fixed in future releases of Pro.
Working with the helpful ESRI support, we found that adding just the layer from the service into Pro, labels are possible. In this instance: https://landscape1.arcgis.com/arcgis/rest/services/USA_Roads/MapServer/2