Vandergrift surname appears in Bensalem Bucks Co. in church records in 1710 all are descendants of Jacob Leendertsen and Rebecca Fredericks. All of Jacob's and Rebecca's children are recorded as "van der Grist" in New York. There is no clear origin for the name. There is a river "Grift" near U trecht, Netherlands. "van der Grift" records in Amsterdam, Netherlands start end of 17th century. Jacob was son of Lenert/Lenaert Everts and Maritje Pouwels/Poules Lenert (1687 ab/ - by 1657) originates from "Saarlois" (Charlois) near Rotterdam and Maritje marr. in 1609 and had children to 1627. Lenert is not recorded as "van der Grift/Grist" in Amsterdam There is no documentation for his father. There is no documentation for Evert Anthoniusz (or) Van der Grift.
There is an Evert Tonisz marr. Elsje Tijssen in 1598 in Amsterdam They have Giertje in 1599 and "Evert Antonisz" and Elsje Tijssen have Jan in 1603. Elsje Tijssen widow of Evert Tonis marr. Jan Dierixsz in 1605. Clearly no connection to Lenaert born 1587.
The first son of Lenaert Everts and Maritje Poulus is Jan in 1612 and second son is Paulus in 1613. It is feasable that paternal grandfather to Jan was Evert Jansz but there is no documentation either.