i don't think this is possible you can disable the data labels but you can't constantly show them.
However if you need to display the name of the state for example you could use a map background overlay like so
Here are a few links to threads with background layers:
There is no such functionality on native map object. Qlik Sense native map object is quite limited.
Take a look in the QlikGeo Analytics product for enhanced map features or QlikMaps from Analytics8.
Also, If you have a web development skills, take a look on several map extension available at branch.qlik.com. They are open source project, so no fees to pay in advance, but you need a web developer to support them.