If a person's name is Null then how would it break the database? I was reading this article on BBC. It tells a story of a person named Jenifer Null and how she faces day to day problems while using online databases like booking plane tickets, net banking etc.

I am not well versed in databases and I do not use it very often. When I made a website for learning, the server side form validation used regular expressions. From what I remember it would happily accept the name "Null". I have not tried it though.

Could someone explain the technicalities when this situation would occur? Is the form validation just doing a string == NULL or something? Even so I do not think NULL is same as "NULL".
I have seen database interfaces (e.g.  framework libraries) that return 'null' as a string for null columns.  I believe there was a flag that would turn this on or off for debugging.  This flag allows developers to easily determine if the empty field was a result of a null value or an empty value.  This is a bad setting, especially in production, and would explain the issues explained in the article.  

The reverse processing of converting 'null' to a null value should generate an application error for a name field.  I would expect this to be rather quickly resolved.