What do you call the shaft or assembly that the front wheel bearings and rotor mount to on a disc brake system?

 

Spindle

 

That is what I thought, but every time I try to find one the wrong parts come up.

 

On most Oldsmobiles that shaft is actually an integral part of the steering knuckle. Many people will use the term "spindle" to mean the whole knuckle, not just the shaft itself. Since it is not a separate part, that's probably not an issue. If your bearing surfaces are damaged due to a seized wheel bearing, you need to replace the entire knuckle. Tell us year and model and drum or disk brakes.