Isaiah 43 speaks to Israel as a people God created, formed and redeemed. 'I have called you by your name' belongs within that covenant relationship. The passage promises God's presence through waters and fire rather than a life without difficulty.
As we read, we learn about the character of the God who knows and claims His people. Belonging is deeper than a flattering label, and His care does not depend on a season being easy. We can bring our own accumulated labels before Him in the light of the belonging we receive in Christ.
Do not search this passage for a promise that every obstacle will disappear. Receive its invitation to trust God's presence. Consider how your speech, boundaries and choices might change if rejection were no longer the loudest voice describing your life.