So far, named 32nd century ships we got are:
USS
Constitution NCC-31700... (one or two digits missing at the end of the reg)
USS
Cuyahoga* (according to Memory Alpha)
NCC-325019
USS
Nog NCC-325070
USS
Tikhov (named for a 20th century Russian astronomer)
USS
Voyager NCC-74656-J (11th ship to bear the name/reg)
*According to Wikipedia, Cuyahoga is a place name in the US state of Ohio, in the Americas. (That could qualify the name to appear for a predecessor starship in
Lower Decks.)
EDIT:
The new starship classes as visible at time index 00:00 (really) of the ep6 trailer. Gosh, I hope we''l be supplied with official class names.
At 00:14 we see the wreckage of a
Hiawatha-type.
Cardenas-class at 00:24.
Remember the Season 3 trailer, when we saw old Fed ships crash on a trash heap? Looks like they are wreckage already and get pulled into ad-hoc service.