If you go on the Classical tour, you could use the Batavians (like Halcyon Dayz said) as in the Batavian republic or Batavia. You coulduse the Frisians (Frisia or something like that). These Dutch could still identify themselves with the Belgians, so you could even call the New Netherlands Belgium. Other groups that lived in the Netherlands were the Franks and the Saxons, but those are more often linked with other countries like France, Germany or England.
I am not certain how you Germany is called in German, but in theory you could call it something like Dietsland/Dutchland. Dutch/Deutch/Diets means something like "of the people" which would be a good name for a republic.
Alternatively you could call it after something American, "verenigde staten van Amerika" could work (Dutch translation of USA), perhaps you could name after the leader of the resistance (or an imprtant republican figure of the past, like Brutus). You could name it after some Indian tribe, Columbus, a river, the general name of America in your timeline etc.