Is there a specific name given or applicable to such genre of movies ?How do you otherwise search for such movies ?
It is exactly defined as
hyperlink cinema as films where the characters or action reside in separate stories, but a connection or influence between those disparate stories is slowly revealed to the audience
I got the answer from ankit's link though.
These kind of films are called Anthology film. From Wikipedia:
An anthology film (also known as an omnibus film, package film, or portmanteau film) is a subgenre of films consisting of several different short films, often tied together by only a single theme, premise, or brief interlocking event (often a turning point). Sometimes each one is directed by a different director.