For the first scenario, it would depend on the type of victory. Based on West Virginia existing at all, the CSA would have to win after 1861 and can't be decisive enough (defeating Union armies on all fronts, UK and France sending ships and troops prior to Antietam, etc.) for WV to be demanded in peace negotiations.
Union control was spotty prior to, and indeed after, WV statehood, but to limit it to Wheeling or even just the Ohio valley before 1863 drastically minimizes its importance. WV was not just a ploy by Lincoln to split VA, there was significant support and no significant Confederate victories to contest it. Heck, Alexandria, which is on the Potomac and had once been part of the District of Columbia before retrocession, was even the capital of the loyal Virginia government for a period before statehood.
In fact, in a Confederate victory, I could even see WV getting larger, including many the counties north of the Rappahannock from which the Union Army would refuse to withdraw. Unless Confederate troops were able to retake the area, it seems unlikely it would just be given back. Mosby and other partisans were hardly enough of a force to make the Union give up. And without Lee's troops on them, I particularly have difficulty seeing the US giving up the Arlington Heights, the hills across the Potomac from DC.
Kanawha was one name bandied about by the loyal Virginia government, but was eventually discarded in favor of WV because of the desire to maintain the historical legacy of that name. And lots of people probably thought Kanawha was dumb. If the South won independence, they would probably want to directly maintain that legacy and stick with just “Virginia.”
In your second scenario, I think such a crushing defeat of the South would have to come early in the war to keep there from being a separate WV, maybe resulting from a CS route at 1st Manassas or McClellan successfully taking Richmond and driving into the Carolinas in an improved Peninsular Campaign. In that case, I could see VA staying united, but their differences weren't as drastic as the Germanies. The Unionist (and probably Republican) government put in place in Richmond would be far more attentive to small farmers and craftsmen, work with the Federal government to punish large slaveholders and others responsible for the war, and might even move the capital to somewhere more central, such as the Shenandoah Valley. Just remember, the USA won a pretty crushing victory in OTL, and the Virginia's were not reunited.
One important note though, in any USA victory, even a crushing one, before 1863, slavery will not be unilaterally abolished the way it was in OTL.