How to remove your Last name from Facebook
Whatever reason you have for hiding/removing your Last name on Facebook I think you should be able to do so if you want it BUT, this is not a straightforward process to do.
I'll describe a trick you can do to achieve this result (at least it works as of 15/01/2017).
*You can click on the links in provided steps not to get lost on the "mbasic" Facebook's version(especially as you'll see the interface in the Tamil language).
- Configure your browser of choice to use a proxy from Mumbai
- Go to https://mbasic.facebook.com and Log In into your account (you'll probably have to confirm through email or phone that you're the one trying to Log In from India)
- Change your Location to Mumbai
- Change your Language to "Tamil"
- Change your name as desired and submit the form (you might need to confirm by entering your password)
- Change your Language and Location back to your preferred one
- Remove your proxy configurations and use Facebook as normal