Removing first name on request by supervisor: how to avoid complications in the future
Use the name that you wish to be known by within academia. For the next 40 years (depending on age and career), you will build a reputation attached to your name. That name will be on your papers, announcing you for presentations, on your name tag at conferences, as the author of any books you publish and for many other uses.

Your supervisor is not asking for a trivial change for his or her convenience, your supervisor is asking for you to either give up your preferred name throughout your career, or to have multiple names on publications. While it is certainly fixable to have multiple names, it is harder to ensure you get credit for all your work.

You could perhaps ask why your supervisor wants you to use a different name. There may be a good reason in which case you can take that into account in your decision. Since you have a long name, do people use the full name when addressing you? Would it be reasonable to use perhaps a shorter version of your first name if that's how you are known?