Why are the two dots on the e in Wassenaër? Wassenaer is the old Dutch spelling for the town of Wassenaar. I couldn't find references to justify the use of the two dots.
We have added some early references with the spelling "Wassenaër". While you are correct that in Dutch it is "Wassenaer", the French spell the name with ë, which Verdier seems to have followed.
The use of the diacritical marks "Schwa", "umlaut" shown as two dots over an "a" or "e" usually is meant to show a stress on that syllable to reflect how it actually sounds when spoken. This usage is reported to have been popularized in the early 1800's by the Grimm brothers.