In the TLs where Manifest Destiny is wholly successful and the USA eventually absorbs Canada (it joins the ARW), Mexico (wholly annexed after the MAW), Cuba (conquered before or after the ACW), the Dominican Republic (peacefully annexed after the ACW), and quite possibly other chunks of the Caribbean, Central America, and South America, which regional names would be devised by Americans to give an handy label to the various sections of their sizable country ? Several OTL ones do not make too much sense with a continental union.
Lets stay in North America, the Caribbean and Central America (South America stays independent).
Region One: The North East (as in OTL), but it would also include the Maritimes and Lower Canada (Quebec).
Division One: New England (Plus Maritimes)
Division Two: Mid Atlantic
Division Three: Lower Canada
Region Two: The South (as in OTL), because of its history people would still identify it as such though maybe it is referred to as the South.
Division One: Upper South (including South Atlantic)
Division Two: Deep South (or Eastern Gulf)
Division Three: Carribean, including the Eastern coast of Yucatan (OYL's state of Quintana Roo)
Region Three: Upper Mid West
Division One: East Central, The Great Lakes Region including Upper Canada (Ontario).
Division Two: North Central, Canadian Prairies, and Northernmost Midwest States.
Division Three: South Central, Southern midwest including Arkansas and Oklahoma.
Region Four: South Mid West, Texas, The Southern Rockies and Northern Mexico (Rio Grande Rep, Chihuahua)
Division One: Rio Grande Texas and Northern Mexico
Division Two: Basin, Nevada, Utah, Arizona New Mexico Chihuahua
Region Five Pacific:
Division One: North Pacific, Oregon to Alaska
Divsion Two: Mid Pacific, Cali including Baja, and Sonora
Division Three: South Pacific, the Mexican Pacific up to Oaxaca.
Region Four:Central America
Division One: The Gulf, Veracruz, Tabasco and Yucatan
Division Two: Central Mexico
Division Three: Central America