No need to "register" your work for copyright.

"Currently, all copyright-eligible works created on or after January 1, 1978 are protected for 70 years after the death of their author. This right is granted automatically by the Copyright Act of 1976, which established a 50-year protection period after death, as well as Amendments such as the Copyright Term Extension Act of 1998, which extended post-mortem protection to 70 years. This also applies to joint works created by multiple authors, where the term of protection is 70 years after the death of the last living contributor."

source: https://copyrightalliance.org/what-happens-to-your-copyrights-after-you-die/