gear oil.

I use their Series 2000 75w-90 in my race car and 75w-140 in my dually.
These also have a limited slip additive in them!

Amsoil source.

Some gear manufacturers suggest breaking in the gears with conventional gear oil, then changing it to whatever you decide on using. That's not a bad idea because the protective coating on the ring & pinion actually isn't good for the bearings after it wears off!