What bugs me with this locution is that it leads one to believe the
river didn't have a name, when it's had lots of perfectly good ones
before "Hudson." (I am less familiar with Champlain, but I'm assuming
it's the same.)

I like to tell people, "In 1609, Henry Hudson sailed up the
Muhheakan'tuck River. Later renamed for Hudson...."

-- 
James Nevius
http://www.walknyc.com