Belgium was not an independent kingdomuntil after the Napoleon was sent back to France, the HRE was disbanded and the 9-year war ended, This I think was around the mid-1800s when it finally ended.
This is important to understand as Anthonius Laenen, the father of the American Van Pelt line, was born in 1624 and raised in a diocese owned by the HRE Thus by the time your family came to America Anthonius had been dead over 250-years. It was his children who honored their father and ancestors by adopting the Dutch phrase "van Pelt" as the fixed surname Van Pelt.
The first Van Pelt surname did not appear in the earliest records held by the Chief Archivist at Hasselt that I reviewed until about 1701. I could find no connection between this Van Pelt and Laenen families.
You must also understand that after the English invaded the New World - more than 100-years before the Revolution - a royal English law banning Patryonymic names and demanding a fixed Surname throughout all the Isleswas in place for many years before your ancestor set sail. By 1850 most of the world had adopted the fixed surname. I followed my Dutch to about the year 1500 and then about another 600-years of land history.
Leaving from Amsterdam aboard a wooden schip was not uncommon in the mid-1600s for by that time Amsterdam was one of the busiest ports in the world. Not only that but Over Pelt was on a main trading routed between Cologne and Antwerp. lt was not that difficult to get to Holland, anyway, as they were already in Gelderland where their children were baptised in the protestant church with the Patronymic second name.