Hey there!
Yeah, that’s totally possible — and depends on how you’d like to go about it.
For example, you can append the category name to the event title itself using a snippet like this:
https://theeventscalendar.com/knowledgebase/add-category-prefix-to-event-titles/
Or, you can always override any one of the calendar templates with your own code and use the tribe_get_event_taxonomy() function to display the category for a particular event where you would like it to display.
Either way, please do check out our Themer’s Guide for more info on how template overrides work with the calendar — it’s a great place to start with customizations:
https://theeventscalendar.com/knowledgebase/themers-guide/
Cheers!
Geoff