UNIQUE - way to have unique rows in table?

Question

I have problem with unique rows in db table, now it is posible to do that:

id  | Name  | LastName  | City
-------------------------------------
1   | John  | Moore     | London
2   | John  | Moore     | London

when i use UNIQUE attribute in all columns i have errors inserting second Moore even it is different Name :/

how use UNIQUE (or maybe INDEX?) to do something like that in my table in db:

id  | Name  | LastName  | City
-------------------------------------
1   | John  | Moore     | London
2   | Jake  | Moore     | London
3   | John  | Keen      | London
4   | John  | Moore     | London //but good error when inserting the same row

Sorry if question is easy, but i am beginner at sql, and have problems with find some good example with using a UNIQUE like a want:/ or maybe I must just before inserting a new row selecting a table from db and check if it exist?

Answer 1

Remove the unique index on the individual column and make it on both columns together, like this:

CREATE UNIQUE INDEX ixFullName ON yourTable (LastName, Name);