I may have found a way to rename a pinned tab. I am using Safari in Macbook with El Capitan.
Clarification: I didn't renamed a pinned tab. Rather I unpinned the tab then came with a way to pinned again with a different name.
For example, I had three pinned tabs all named "G": Google Keep, Google InBox, Google Calendar. I was able to pin them as G, I, and K. Here is the method I followed:
1. Unpin the tab and close the web page.
2. Look up the web page in Google (or another search engine)
3. Open the page.
4. Save the page on your Favorites bar; but "rename" it -- (I named "Google Keep" as "K").
4. Now click on the newly renamed link to open the page.
5. Now pin this page. It should be pinned with the new name.
I hope this method will work for you.