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In the United States, the surname Schuyler is normally pronounced the same way as Skylar or Skyler. There was a Schuyler family that was very prominent in the early history of New York State, which was originally settled by the Dutch. There was a Vice President of the United States in the 19th century named Schuyler Colfax, named after this family, and his given name was pronounced that way.

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http://bioguide.congress.gov/scripts/biodisplay.pl?index=C000626

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The spelling Schuyler was in regular use for the first name before the alternatives Skylar and Skyler became common. There doesn't seem to be any reasonable objection to me to seeing Skylar and Skyler as modern respellings of Schuyler.