I am attempting to change the email a custom contact form is sent to based on what selection the user makes when filling out the form. Is there a way to do this in Drupal 8?
There isn't a way to make behave like its D7 incarnation without some custom code. You might, however, find this issue on d.o. useful; it contains a patch that adds a customizable block which lets you select a contact form (and thus recipient) to use.