Can the name on a birth certificate and death certificate be different?

Yes, if you get married or change your name.

Also, many people use variations of their name, especially with different spellings. A person born as Lewis may use Louis as his name as an adult. Over the course of a lifetime a person's name may become quite different from the name on their birth certificate regarding spellings and name variations. This issue is often encountered when examining the title to real property in the land records.