He would have been happier to have nothing named for him and no statues erected. Apparently Woodrow "Author of Southern Revisionism" Wilson didn't give even half a fuck about the dead man's wishes. Robert E. Lee, Jefferson Davis, and a bunch of the other generals all specifically said that no monuments or commemorations should be erected to honor them, as they recognized they were traitors.

Wilson is the one that refounded the KKK, helped fund the filming of Birth of a Nation, showed said travesty of a movie at The White House, used his Yale credentials to write Southern Revisionism, used his power as president to erect said statues and change the names of places and monuments, and segregated The Federal Government. That's just looking at his domestic policies. Wilsonian Doctrine gave us the Forever Wars that have ensued since, and that could easily be argued to be the least damaging thing that asshole did.

Wilson is only second to Jackson for worst president ever, and that's only because Jackson paid off the national debt, and caused the worst depression in US history. Deepest by economic percentage, though not dollar amount, and longest by over a decade. They both committed their own flavors of genocide against the Native Americans.