No, it is not possible to change the URL of a Story Map tour in ArcGIS Online. This is by design. ArcGIS Online does not allow custom URLs for Story Map.
There are hosted and downloadable versions of the Story Map template available. The downloadable version allows more customization and alteration compared to the hosted version. Refer to the following link to learn more about the different templates in Story Map Classic: What Kind of Story Do You Want to Tell?
Note: The need to customize the URL of a Story Map tour may arise when the link is included in print publication or public presentations for businesses or personal reasons.
A possible workaround for this issue is to redirect the Story Map Tour to a private server from the Esri server. This is accomplished via the downloadable template of Story Map. Host the downloaded application code on a private server, may it be a personal server or an organization server. Configure the Story Map application with the same story ID that was used in the web application to avoid recreating the entire story.
In addition, there are a variety of popular short link services such as 'bit.ly', 'Cloudapp', 'awe.sm' and many more services that help create and customize links for free.
Note: These services do not belong to Esri and Esri does not provide any recommendations or support for the use these services.