Well, Andrea Doria isn´t that dark: we owe him not being muslims today.
But the others are a bit obscure. True that names like Tirpitz, Bismarck, Carl Vinson, Hans Lody, John Stennis, etc. are not ideal. I wonder if in 100 years time people will know who was some Ronald Reagan whose name was bearing in an ancient aircraft carrier. Perhaps Nimitz or Spruance aren´t that bad because they feature in great battles text books. Names after battles don´t sound bad neither: Midway, Saratoga, Coral Sea, etc.
The Americans didn´t had a bad idea naming their BBs with State names: Montana (

), Iowa, South Dakota, etc. I think they asumme that their today´s BBs are their Submarine fleet so they named after cities.
But for an American warship name the one (and the only) is:
ENTERPRISE. (Don´t forget that probably an Enterprise will boldly go were no man has gone before)