English text Wikipedia about Leeuwarden https://en.wikipedia.org/wiki/Leeuwarden Listen to the Dutch pronunciation of Leeuwarden. (Frisian: Ljouwert). Also in that article, the origin of the name. History of the city including a part about the Jewish community.
There were/are, besides the Frisian language in different dialects and local languages different variants of the name, so pronunciation may vary. Leeuwarden en Leuwarden is just a matter of spelling.
It's beyond me how Leeuwarden as a surname hints them to being Levites.
To Tanya Williams: maybe it's not a matter of changing surnames, but using, or being registered with different surnames in different context. I researched a Cohen family; while some of them appeared in Amsterdam burial records as amesfort or the like, others didn't (though they all lived or had lived in Amersfoort and used the name Cohen). A family de Jongh (de Jong, de Jonge) that used that surname since late 1600's but remained Rintel in Jewish records). And of course, in Europe early 19th century everybody had to have an official surname, and within families different surnames could appear.
To Pieter Hoekstra: Westfriesland is the name of a region in the northern part of what is now the province of Noordholland. Originating from the time they were connected with nowadays Friesland. https://en.wikipedia.org/wiki/Friesland#/media/File:Frisia_716-la.svg
Later and now https://en.wikipedia.org/wiki/West_Friesland_(region)
I can understand though why the name west-Friesland for the Dutch part of Friesland is also used as opposed to Ost-Friesland in Germany.
Loes Buisman, Amsterdam