SQL update set column = @ parameter
You're close, but when you introduce two tables, you have to be consistent with the alias.  So
at the declaration of the update statement, you'd want to start with: 

UPDATE ua1 
SET properties = 'Charlie' 


Then create a from clause just as you would with a select statement, declaring your aliases:

FROM UserAttribute ua1 
    INNER JOIN UserAttribute ua2 
        ON ua2.UserID = ua1.id 
WHERE ua1.name = 'Contact';