The Bolivarian Republic thing was created by Hugo Chávez, if alt-Bolivia get that adjective, it would be totally anachronistic.
Unless of course someone else came up with it earlier? It's not impossible seeing as Bolivar was a distinct figure, but I guess it's not necessary either.
Potosí was the main reference IOTL for old Bolivian land so i would go for a Republic of Potosí
Hadn't Potosí sort of fallen into decline by the 1800s?
Depends of the circumstances, but if Simon Bolivar doesn't have an influence there, it should just be Republic of Charcas.
This is an important point actually seeing as I have actually planned for San Martin to liberate Bolivia alone so there's no real reason for it to be named after Bolivar. I guess I wasn't really thinking when I made the poll!
This. Many Spanish American lands changed their colonial name for a reason (New Spain-Mexico, New Grenada-Columbia, La Plata-Argentina) and Alto Peru only gives Peru more attention.
Peru, Venezuela, the Dominican Republic, Puerto Rico, Cuba, Guatemala, Costa Rica, Nicaragua and Chile all still have their colonial names and Colombia was still known as New Granada for some time after independence (following the end of Gran Colombia, it became the Republic of New Granada and then the Granadine Confederation), so actually at times the majority of countries didn't change their names. Argentina was early on know as the United Provinces of South America/the Río De La Plata so it did partially keep the colonial name as well until it fell apart.
Picking Sucre with an 1812 POD is kinda weird (the general Sucre who is the namesake of that city only rose to prominence in 1824), so that's out. Alto Peru I think is a terrible name, mostly because I just dislike countries that identify as having been part of another country (s. South Sudan)...
So only Charcas and its variations and Chuquisaca and its variations are possible, though I'd pick Charcas since it is connected to both the indigenous and the colonial past of the area, while Chuquisaca is closely connected to the early 19th century only.
Also I picked the Bolivarian Republic of Charcas option, because I find it to be kinda funny, to be honest, even though that sort of naming is too connected to Hugo Chaves IOTL.
The POD for the story as a whole is 1812, but that doesn't mean that Bolivia gets independence in 1812, so Sucre still has time to come into prominence (the POD wouldn't have any initial butterfly effects on South America).
Still, Charcas and Alto Peru look to be the two most popular based on the votes.