Can an Uber driver see your destination?

No, Uber does not allow drivers to see the destination. There are exceptions

(This was covered under the question, "How can you determine the riders destination before accepting the ride? (Uber)"

The basics: The driver cannot see the final destination of the rider until he or she accepts the ride.  This is to prevent drivers from cherry picking the rides they accept. 

Exception: Since earlier in 2018, Uber and Lyft are both experimenting with a feature where the destination address and/or estimated trip length are displayed *before* the trip is accepted.  The drivers have to satisfy 

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Uber Driver, CEO of TaxiFareFinder and Unleashed, LLC