FARSCAPE actually gave us a good one. "Welcome to the Federation starship S.S. Butt Crack." (smacks own ass) John Crichton, "SELF-INFLICTED WOUNDS PART I: COULD'A, WOULD'A, SHOULD'A"
I wonder what the criteria are for figures who have tarnishes or outright disasters on their record. Consider Admiral Leyton, the guy in DS9 who tried to usurp Federation authority in the name of fearing Dominion Founder infiltration on Earth. I do believe the implication is that Leyton did perform meaningfully good things earlier in his career before making admiral, so would any of those accomplishments outweight his treason in the long view of history? Concordantly, an insignificant spoiler from the final season of Star Trek: Picard: Spoiler PIC 3.09 introduced the U.S.S. Jaresh-Inyo (NCC-75020), a Sovereign-class ship in 2401 obviously named after the Federation President who failed to stop Admiral Leyton's attempted coup. The non-canonical novel Articles of the Federation extrapolates that Leyton's attempted coup was the decisive factor which cost Jaresh-Inyo reelection that year.
Incidentally, the 2000s novel series I.K.S. Gorkon featured the Qang-class ("Chancellor-class"), the first 12 of which were naturally named after Chancellor Martok's 12 most recent predecessors, including Azetbur despite how many people during and after Azetbur hated her leadership just because she was a woman.
Doubtful. The UK might be tempted, since he went over to them, but it would probably be deemed not politic, them being our closest ally and all.
I would imagine that Leyton's attempted military coup would invalidate him from receiving the honor of a starship christened in his name. I see no reason why Leyton's sin should preclude President Jaresh-Inyo from receiving such an honor, however. Well, one would hope that the Federation would never have a president as bad as those two. The United States Navy has never, and will never, commission a USS Benedict Arnold.
Lee may have been a confederate but I would hazard a guess that he still has more honor to his name than Arnold, who was a flat-out traitor.
It would have been interesting if the USN still had a USS Robert E Lee in service recently... the Navy considers renaming boats unlucky, but they'd probably be under huge pressure to do so.