Occam's Razor suggests that your examples are named after women
As an example, let's take the USS Nightingale. There are lots of people who have that surnames including William Nightingale, Mark Nightingale, James Nightingale, or any of dozens of other Nightingales.
Occam's razor suggests that the simplest solution is the correct one. I think that the simplest solution is that Starfleet names their ships after the most famous person to bear that name, or the one who most embodies some characteristic Starfleet aspires to.
Therefore, it's almost certain that the USS Nightingale (a search-and-rescue vessel) is named after Florence Nightingale, who is both famous and known for helping injured people, as a search-and-rescue vessel would do.
Barring any direct in-universe explanation for the meaning of a ship, or any out-of-universe information from the writers who introduced these ships, this is likely the best we're going to get.