John White's journal of his voyage to the New World was written in 1587. In this journal he list the names of all the men, women, and children who arrived safely to the first English settlement in America. Roanoke settlement it was called, and it has be named "The Abandoned Colony".
The list is arranged first by "Men", then by "WOMEN", then by "BOYS AND CHILDREN", then by "CHILDREN BORN IN VIRGINIA", and finally by "SAVAGES WHO HAD BEEN IN ENGLAND AND RETURNED HOME TO VIRGINIA". One hundred and eighteen names are recorded. The list of men seem to be organized according to prestige, with John White heading the list. Anaias Dare, the son-in-law to John White, is listed third. [Remember, Virginia Dare, his daughter, was the first English child to be born in America.] Elyoner Dare is the first to be listed among the women.
There are three with the surname JONES listed. First is JOHN JONES [of course it had to be John] He is listed at number 14 among the 90 men recorded. Griffen Jones falls all the way down to number 85. Jane Jones is listed as number 6 among the 17 ladies recorded. It does not record the relationship between these folks, but the colony was family oriented. Since Jane Jones was in the top 3rd of her group, and John Jones was in the top third of his, I suspect they were husband and wife. Griffen Jones may or may not be related.
So there you have it. The first JONES "...who arrived safely in Virginia and stayed there to live, 1587, in the twenty-ninth year of the reign of Queen Elizabeth."
John Jones, Griffen Jones, and Jane Jones were their names.
Reference: "The New World, The First Pictures of America", Edited by, Stefan Lorant, by the Beck Engraving Company, for Meredith Press, 1946. The list is given on pages 165-166.
The numbering system was my addition and not part of the original documents.