Can’t we get a more metal-sounding name, like Razorspine or the Blood Wastes?
But make it a limited-time contract, like some sports teams and arenas do.
**Off-Center African Republic
Sudan Sudannadanna
Fitzroy
PEOPLE’S KINGDOM OF ECSTASY AND WRATH!** (including exclamation point)
**Republic of the Congo III: Congo Harder
Wallyworld**
Then their banknotes can use this font. (And artwork, for that matter, as long as you put a dude with a guitar in it)
That would be Ȑazørspïnę or the Blööd Ŵastes ? 
Anything with “Sudan” in it is unimaginative at best and strikes an oddly “old” note for a country and people that have suffered under that name.
I think “The Nile Republic” sounds rather elegant and would be fine if the country actually contained more of the Nile, and the river were not so firmly associated with Egypt. If Egypt and a substantial portion of Sudanese territory were ever to be reunited, it would be a good name then, for that country, which probably wouldn’t include this one.
Besides colonial connotations, “Equatoria” just sounds like a hypothetical country, not a real one.
The ethnic and lingual demographics are too splintered to find anything useful there.
Realistically, I think “Juba” is the best option. (The capital can be Juba City, if you like.) I suspect that old Sudan will experience further territorial adjustments in years to come, and it is often practical to refer to shifting power and territory bases by nominal centers (as seen with “Khartoum” to mean not just the capital city and the official state apparatus, but also the idea of allegiance to that center, e.g., “the Janjaweed are soldiers of Khartoum.”)
Sudan II: Electric Boogaloo
Rock on!!