I have to agree with Isabella. Baltasar Carlos surviving almost certainly means that he will marry Maria Anna of Austria. Remember that France still remained at war with Spain in the aftermath of the Thirty Years' War (for a long list of reasons) until the Treaty of the Pyrenees was signed in 1659, at which time Louis XIV and María Teresa were betrothed to seal the agreement.
Now, Baltasar Carlos may also end up remarrying at some point in the future if Maria Anna predeceases him without having produced male issue—and that could very well be to a French princess. This could go either way. Some may disagree with me, but it's worth remembering that Baltasar Carlos and Maria Anna would have slightly more generic distance than she and Felipe IV, and that in OTL, despite the disaster that was Carlos II, the couple managed to produce Margarita Teresa as well, who, despite all odds, was born physically and mentally healthy. There is no reason why Baltasar Carlos and Maria Anna can't do the same and produce a healthy son—though I grant you this is by no means a certainty and given the reproductive track record of the Habsburgs, the majority of their issue will probably die very young. In any case, as I have said, Baltasar Carlos may also end up remarrying and siring an heir.
As for how Spain would fair, definitely better than in OTL. The rule of Maria Anna and her favourites was disastrous, to say the least. The success of Baltasar Carlos will depend on:
—His ability to stabilise Spanish finances and prevent the bankruptcies that occurred OTL
—His ability to enact administrative reforms and centralise power against the opposition of the nobility, Church and various other privileged groups and institutions of the Spanish kingdoms (remember, 'Spain' at this point doesn't even really exist)
—His policies concerning relations with France and his brother-in-law Louis XIV, which will be quite different than OTL (for instance, butterflies will ensure in that the War of Devolution does not take place, at least for the reasons in OTL)
—His ability to produce an heir and secure his dynasty
As for his regnal name, I would assume 'Baltasar Carlos (I)' is most likely.
Amitiés,
Endymion