What is the term for a person with same first and last name?

They are very likely informally termed tautonyms or as the Wikipedia page tells me, linguistically called reduplicants. There's a page full of people with reduplicated names including:

  • José José
  • Justo Justo
  • Kelly Kelly
  • Lisa Lisa
  • Thomas T. Thomas

The term is not used solely for names with reduplicated first and last names, but also for other variants such as Jar Jar Binks or Richie Rich.