This blog may help you to change the existing URL when you change the Document Library.
Normally, when we create a Document Library in SharePoint, the URL gets created based on the library name like http://servername/sites/libraryname/allitems.apsx
So when we change the Document Library title by using Library settings -> Title & Descriptions, the Document Library Title may get changed but the URL never gets changed and it would be in the old library name.
If we want to rename the title of List/Library with URL change, we need SharePoint Designer.
But here, we have some other ways to change the URL and Title of the Document Library and please note, this will work only for Document Library.
In my demo, I have one document library called Shared Documents, so I renamed it as Documentum using Library Settings -> List Name.
Here, you can see that I have changed the Title but URL is still the old one.
So what I am going to do now is to open this library in the Explorer view.
Now, we are moving one step backward to view the library name.
So, I have changed my Library Name from Shared Documents to Documentum and refreshed my existing web page.
Now, I am getting a 404 error which means the resource (URL) has been renamed or moved. Again, I am navigating to the site content and selecting that document library and checking the URL now.
Finally, the Library title and URL has got changed without SharePoint Designer.