The profile you linked has a birth date of 1602 at a location called "North Farnham Parrish, Richmond, Native American Lands". I can say with 100% assurance that the place was not known by any of those names in 1602. If she was born in the vicinity of Richmond, Virginia in 1602, I have to assume that she was a Native American, so her name at birth would not have been Elizabeth.
If this is a native woman who lived in the area that later became Virginia, my preference would for the text section (which hasn't been created yet) to explain that she is thought to have been a woman of a particular Indian nation (include the name of the nation or tribe) who would have been born in the vicinity of what later became Richmond (or perhaps that later became Wise County -- this isn't clear from the information provided), Virginia. For the location entry in the profile data field, I'd suggest "Virginia" as an approximation.