On the (pre)marriage record ("ondertrouw") between John Fletcher and Josina Sacharias his name is listed as "Jan Moysesz," born in "Santwits, Engelant," and states that he was the son of "Moses Fleteker." The surname "Fletcher" doesn't seem to have stuck to John, the son of Moses Fletcher, even if that was his LNAB. John's son, Sacharias, appears to use the patronymic "Jansz," or some variation of that, in his own records. It's a bit of a toss-up what Sacharias LNAB should be because his baptism record provides his given name and the names of his parents, Jan Moses and Sijntge Sacharias. His LNAB could be either "Jansz" or "Jansen" based on other records from the period between 1645 - 1695.
Per English naming conventions, a wife usually takes the surname of her huband when the become married. In Dutch naming conventions a woman keeps her LNAB throughout her life, but may be referred to as the wife of (husband). If Josina moved to, and died in, England then her current last name may be Fletcher, but if she died in the Netherlands then her current last name should be Sacharias, the same as her LNAB.
It's going to be a similar story for the other Dutch-born grandchildren of Moses Fletcher. Based on the few records I looked at, they were using patronymics rather than a family surname, so you'll get LNABs that change each generation. The Koets family may be an exception; here the name appears to be a surname for at least two sequential generations.