By googling I have discovered the French name - Ignard - which may be the source of the American name Enyart .
In French and Italian -- gn -- is pronounced -- ny -- like the Spanishn with tilde and Portuguesenh ..
So Ignard would be pronounced as our Enyart or Enyard .. with the y sound.
Enyart does not seem to be a variation of Engard or Engart -- where theg is hard - as in -go-.
So my personal guess is that the name Carel Enjoert was a modification of the name Charles Ignard .. and - Yellis Enjoert - or Enyart would be a variation of the French --Gilles -- used later as Silas ..
They may have been Dutch or Flemish, but the name seems French...