Right, so she was not owned by the US government (that is what I meant above, but I see I was not making myself clear by leaving out 'government'). She was owned by a private company. I think the private company was Spofford, Tileston & Co. of New York. See Link 1, Link 2, and Link 3.
Link 1 indicates she was contracted by Spofford, Tileston & Co. to the New York & Havre Steam Navigation Co. for two voyages in 1854. Link 2 indicates she arrived in New York from Charleston on January 20, 1861, with passengers and merchandise to Spofford, Tileston & Co. Mail service was not mentioned on this notice of 1861 arrival.
Link 3 indicates the Nashville was part of a fleet owned by Spofford, Tileson & Co. and James Adger of Charleston. Apparently Adger died in 1858, but the James Adger II Company of Charleston continued to run the ship James Adger between Charleston and New York Link 4.
The ship, the James Adger was seized in New York at the start of the war, apparently then purchased by the US, then converted to US Navy service. Interestingly, Link 4 says the James Adger was used during the war to pursue its once sister ship, the Nashville.
Nor did I intend to imply Nashville was a US Navy ship.
Nashville: a civilian ship, belonging to a large shipping company originally owned entirely by New York investors (now including some from Charleston), registered in the United States, doing both commercial and US government business, and normally flying the American flag, on routine passage from New York to Charleston.
Due to the "peculiar circumstances" of early 1861 -- or perhaps simply because it's then dark -- Nashville is not flying her normal US flag. This is not at all unusual for the time. Other US ships in Charleston are reported as flying no flags. Challenged by Harriet Lane, Nashville raises the US flag and then waits until the bombardment of Fort Sumter ends.
I'll say again: all of this is of no importance, except in the context of various claims that Harriet Lane fired the war's first naval shots at Nashville. If Nashville was still a Union registered ship, about its normal commercial & government business, then Harriet Lane's challenge was simply routine law enforcement, and in no way an act of war.