Is copyright registration required?

No — registration is not required for you to own your copyright; that happens automatically when you create the work. You can publish with a proper copyright notice and no registration at all, and many authors do.

Registration (for example with the U.S. Copyright Office) is optional and mainly gives you stronger legal footing if you ever have to enforce your rights in court. Whether it's worth it depends on your book and country. This is general information, not legal advice — if enforcement matters to you, ask a qualified attorney.