If it were up to me, the controversies over statues, monuments, street names, and building names would be decided like this:
Every such icon that was located on government property would be considered the collective property of those who currently live in a local community, and who currently pay taxes to maintain the local community. To the degree that the presence of such icons is contentious, a local referendum would be held to determine whether or not to remove them, with a majority rule. If the local community voted to remove these items, they would then be peacefully sold or donated to either another local community that wanted them, or to a museum (preferably one that was private or operated by a non-government organization, or a least a public museum like the Smithsonian that is dedicated to general historical preservation).
Individuals and private groups could have whatever icons on their own property they wished, including statues of Hitler, Mao, Pol Pot, or Ted Bundy if they wished.
Many of the southern cities where Confederate monuments are located are now majority black, with a large minority of white liberals, so it makes sense that such monuments may not currently be appropriate for such localities. So just move them to some rural white redneck communities where they might be more wanted. Given that Mount Rushmore is located on what is rightfully Lakota territory, it makes sense that the folks there wouldn’t want a commemoration of Teddy “the only good Indian is a dead Indian” Roosevelt nearby. On the other hand, Andrew Young, a former aid to Martin Luther King, says he has no problem with the Confederate monuments on Stone Mountain, Georgia (although that’s just one man’s opinion).
If people in a local community want to change the names of streets, schools, or buildings named after “offensive” historical figures, that should be a local concern as well to be debated, argued out, and resolved by the interested parties at the local level. If a locality wants to have such landmarks named after members of the Manson Family so be it (e.g. Squeaky Fromme High School or Tex Watson Boulevard).
As for private, non-governmental, or semi-independent institutions like businesses, sports teams, universities, entertainment companies, etc., every one of these should have whatever policies they prefer. If a liberal university like Princeton no longer wants to commemorate Woodrow Wilson, fine. If the Washington Redskins no longer wish to honor their racist founder, fine. If entertainment companies no longer want to distribute films or TV shows with “blackface” characters, fine. If the Dixie Chicks want to change their name to the Chicks, fine. Meanwhile, if a Catholic private school wants to commemorate Torquemada, so be it. If a Mongolian-American Association wants to commemorate Genghis Khan, fine. If a sports team wants to call themselves the LA Serial Killers or the New York Pedophiles, so be it. If someone wants to open a “Racism Land” private amusement park featuring hideous caricatures, I’d say they’re within their rights. If a gay-hating fundamentalist church wants to place a statue of Fred Phelps on its lawn next to a Jesus statue, I’d defend their right to do it. I’d defend the right of the headquarters of the He-Man Woman-Haters Club to maintain a statue of Harvey Weinstein.
As an anarchist, I’d be first in line to defend the right of the “I Hate Anarchists Club” to open a museum to historical enemies of anarchists featuring statues of J. Edgar Hoover or Francisco Franco. In my view, the underlying issue in all of this is sovereignty, jurisdiction, and rightful control over resources, along with freedom of voluntary association.