What is the name of this property in (SQL?) Databases?
If that value is unique and is used to identify a single row in a table ( in your example to uniquely identify a single client record) it would typically be considered a unique or primary key. 

If it has some meaning and you already have a separate primary key it could could also be described as a business key or natural key. 

Without a constraint to enforce uniqueness you cant guarantee the data is unique.  You should be careful to avoid developing with that as an assumption.