Minimal axle break-in takes between 500-1000 miles on a lightly used car, so I wouldn't change before then. Full break-in could take up to 5K miles if the car is used lightly. Break-in is mostly work hardening the gear teeth. Excessive heat tends to anneal (soften) the gears, so you want to avoid that. New gears tend to generate lots of friction initially, so there is some danger of getting them too hot. The syn oils tend to reduce heat by reducing friction, so they are good for break-in. For that first 1000 miles, avoid towing, heavy loads and long runs at high speed (especially in hot climates).
It's often best to break in a gear set in stages. That first 1000 mikes is important, but with a light load, only a small part of the gear faces are being used. With increased loads (from weight, towing or acceleration), some deformation occurs, so those tooth contact areas are increased and those new contact areas need some break in too. So, you start off easy, then you can gradually increase the severity of use, taking care not to let the axle get overly hot.
After break-in, most cars can easily go 30-50K on diff oil, or more, even if it's ordinary dino oil. Ordinarly driving isn't much of a load and doesn't generate much heat. If its a top quality oil, you can go lot farther safely. You're just wasting oil without any real benefit if you change it more often than necessary.
The more hypoid offset the axle has, the hotter it will run naturally. That's an element to keep in mind if you are trying to be cost effective in gear oil choices. An old Ford 9-inch, with a 2 3/8 inch offset, will run some 80-100 degrees hottter than a Dana axle with only a 1 1/8 inch hypoid offset. In normal use the Dana axle will be much easier on the oil, so you can use a "lesser" oil.
Continuous high speeds, mountain driving, loads (carried and towed) all tend to increase axle oil temp. After putting an oil temp gauge on my pickup and monitoring it for the past two years, I will never own another truck without installing one. There were times I could have made some nice "hypoid fries!"