What is the name of this property in (SQL?) Databases? Suppose we query Clients Table by Date of Birth, and one of the returned results being a record having client id = CID1234.

Now if we query the same table for client id = CID1234 we should get the record with client id = CID1234 (maybe client id field is primary key or not, that does not matter). Nobody expects that this query to return no results found.

Edit : Trying to make it clear, lets say the returned record had a fieldX = XYZ, now querying on Table with the fieldX = XYZ should also include a record with client Id= CID1234 , if none of the returned records include such a record then it seems something is wrong.

Although this intuitively makes sense, my question is what is the name of this property and is it specific to SQL databases, or a whole category of Databases e.g. Non-SQL etc. 

Is there a name for data systems that have such a property? Can this be found within Lambda calculus?

My original problem is SOA related, but knowing this a property in SQL databases made me ask it here, the original question is posted here : https://stackoverflow.com/questions/41215546/is-there-a-principal-that-requiers-total-of-possible-enumeration-results-to-add
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.