I don't think that a carrier named "Nimitz" would be perceived as some sort of insult.
General McArthur was revered in Japan; the Japanese granted a medal to General LeMay back in the 1960s; and from looking around the web, there are notes that Admiral Nimitz was active in rebuilding post-war relations with Japan. From the Wikipedia: After the war, he worked to restore good will with Japan -- the nation he did so much to defeat in the War -- by helping raise funds for the restoration of the battleship Mikasa, Admiral Heihachiro Togo's flagship at the Battle of Tsushima in 1905. From the Nimitz Museum: He also worked to restore goodwill with Japan by raising funds for the restoration of the Japanese memorial ship MIKASA and urging return of ancestral samurai swords.
I am pleased to hear that we have worked out placing a nuclear-powered carrier with the Koizumi government. (For what it is worth, Prime Minister Koizumi is from Yokosuka.)