No it is not possible with heatmap question while you can assign labels with hot spot. 

In case you want to use heatmap, you get image in report with concentration of clicks and at report leve you can provide labels to different sections of an image. 

Hi @AnnaM89 ,

You can achieve this by using below way around:
 

Click to write the question text<span style="display:none">Image id =12</span>

Add below code in the HTML view of the Qtext:
 

You will get  data in below format :

 

Hope this resolves your query!!
 

The below JavaScript might also be helpful:

jQuery("#"+this.questionId+" .HeatMapImage").attr("id","imageid");

Thank you all! Tom - your solution worked perfectly!