Name for a united Southern Cone

Just what the title says. Suppose that OTL Argentina and Chile (plus perhaps Paraguay and Uruguay) united into a single country at some point in the 19th century. What name might this country have had?
 
If Uruguay and Paraguay join this country, Brazil may declare war just because of how good this country's football team would turn out to be.

But seriously, Brazil has historically had a lot of influence over Uruguay, so there realistically could be a lot of war between these two countries. If the Sudamericanos become expansionist, they could hold real naval supremacy on two oceans as far as South America goes, including a huge fleet based out of Rio de la Plata. An advance up the coast into southern Brazil wouldn't be difficult with a large enough fleet there to support it.

This is suddenly a very interesting timeline. The geography of this nation makes it one that could easily become the regional hegemon, especially in the days preceding the Panama Canal.
 
Patagonia and Araucania are very specific regions. This portion of South America actually is called the Southern Cone, so there is Republica de Cono Sur. Or they could refer to the Tropic of Capricorn and go with Republica de Capricornio. I like the former though, as the inhabitants (officially called Coneros) would "lovingly" be nicknamed coños.
 
Given it the Macedonia treatment, "Former Spanish Viceroyalties of Rio de la Plata and Peru" or FSVORDLPAP. Just to lower the quality of the timeline.
 
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