A word describes the person whose homeland/origins cannot be assurely identified

In the U.S., where historically race was a more important social distinction than ethnicity or class (or, given the hypodescent standard, even skin color), people who are racially ambiguous are a subject of interest, both in popular (“10 most racially ambiguous celebrities!”) and intellectual (“What Are You?”: Racial Ambiguity and the Social Construction of Race in the US) sources.

By extension, ethnically ambiguous would be a broader application of the concept, and to my surprise, turns up almost the same number of Google.com results. A 2003 New York Times article suggests

ethnically neutral, diverse or ambiguous

I think few people would self-identify as "ambiguous" alone as a description of phenotype, or if they do it would be interpreted as androgynous. Rather, this is a label others apply. People who know they are of mixed descent could self-identify as multiracial (U.S. Census category), mixed race, or multiethnic— but in a modern professional setting in the U.S., calling attention to such characteristics is usually inappropriate and even outré.

For similar reasons, terms like mulatto or quadroon are considered outdated, and may be taken to be offensive.