Last day I ran into an issue (maybe I'll post that later) when I had to rename multiple files in a Document Library that resides on an Office 365 SharePoint instance.
What I did was the following:
Step1 - Add the website to the IE's Trusted Sites
First of all, you have to use Internet Explorer. Open in Explorer mode only works with this browser. Add the website to the trusted site's list then restart the browser. Otherwise it will complain later.
Now browse to your SharePoint Library again.
Step 2 - Open the Library in Explorer
Go to Library -> Open with Explorer
Step 3 - Map the location as a Network Drive
Now that you can see the library in Explorer, you need to grab the URL from the Address bar (ctrl + c) and map a network drive:
Press the ALT + T -> Map Network Drive
Choose a drive letter, paste your path and Finish. You may not want to reconnect the drive at logon.
Now, that you can see your files as a drive you can use your favorite tool to manipulate them.
Step 4 - Use your favorite tool to manipulate the files
I just used cmd to rename all pdf files but you can do much, much more with Total Commander if you have to.
Of course, this method work with SharePoint Server (On Premise) as well.