Combining some examples, I came up with the following query (fields and table names have been anonymised soI hope I didn't insert typos).
UPDATE destinationTable
SET destinationField = t2.value
FROM destinationTable t1
CROSS APPLY (
SELECT TOP 1 'SomeRequiredPrefix ' + sourceField as value
FROM #sourceTable
WHERE sourceField <> ''
ORDER BY NEWID()
) t2
Problem
Currently, all records get the same value into destinationField , value needs to be random and different. I'm probably missing something here.