Yes, editing the Event URL of the event after you already started using it is possible, but it is available to Super Admin or Sales manager role permissions for all account events.
Attention
Kindly note that and all changes made in the Event URL will kick in as soon as you hit the "Save" button.
That is why it's super-important to copy new embed code and update new code on the website where you scheduler is expected to appear.
To make sure your scheduler is always 100% up and running, we've introduced notification that will appear as soon as you edit Event URL and hit Save button.
Here's how to update URL of the specific event
Navigate to 
AI Scheduler → Event page
Select the Event you'd like to edit URL
New Event setup window will appear
Select Event details where URL is
Edit URL and Save
Copy and close newly created code, and embed it in your website
Important note
In case you've decided to change originally set Company name in 
Settings menu, kindly note that any change in the company name will affect the embed codes and URL's of all of your events automatically.
Therefore, if you make such a change, newly added company name will be added to all of your events and it's very important to copy all newly created embed codes and update your web pages.