I am also bothered by this phrase, even though I have been known to use  it.  
The problem for writers is that there are not many alternatives.   You can 
ignore the connection between the place and the name on the assumption  that it 
is obvious.  Phrases like "explored the lake that is now named  after him" are 
more awkward.  "Eponymous river" sounds phony.  None of  the choices sound 
very good to me, although I agree that it time to give name  bearing a rest.
 
David Allen



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