Student or Learner
I hear people saying Lake Michigan. But people say San Francisco River and not River San Francisco. Can I say Michigan Lake too?
No. We say the proper name after the word "lake" but before the word "river." It is Lake Erie, but the Mississippi River.
The name of most British rivers follows the word 'River' - the River Thames. the River Meon, etc.
Please be aware that I'm neither a native English speaker nor a teacher.