This thread about why British carousels usually rotate clockwise is
interesting, but I don't think that has much to do with what they are
called.  I believe there is a simpler explanation.

British racecourses traditionally ran 'right-handed', that is, clockwise.
Although many of Britain's 59 courses have gone 'left-handed', that is,
anti-clockwise; about one third of them still run right-handed, including
the world famous Ascot.  Also, there are still some right-handed courses
in the Commonwealth, (and Japan, culturally influenced by Britain in
the 19th. century).

On the other hand, virtually all American, Continental, and every other
country's racecourses have always run left-handed.

It seems sensible to me, that carousel makers simply built them to
match the popular public image of horses running around a track.

Richard Vance