Question

what is the name of the oldest synagogue in the United States still in use today

Answer 1

The oldest synagogue is called the Touro Synagogue.  It was built in 1763 in Newport, Rhode Island.  It is the oldest synagogue building in North America and the US.  It's also the only synagogue that's from the colonial times.

Answer 2

The Touro Synagogue was built in Newport, Rhode Island  in 1763. 

It's the oldest synagogue building still standing in the USA, the oldest surviving
synagogue building in North America, and the only surviving synagogue building
in the U.S. dating to the colonial era.  It was declared a National Historic Site in
1946. 

It was used only occasionally during the Nineteenth Century, but now is used
regularly, and has several year-around programs.