Q:

What is this time describing noun called?

A noun for when something happened is occasion. A noun for how long something took is duration. 
But how would you describe an event that happened at a certain time after an occasion?
Example:

The movie started 7:15 pm on Sunday 15/3.
The duration of the movie was one hour 35 minues.
Three minutes into the movie a guy showed up.
45 minutes into the movie I left the cinema.

Is there a more general noun to describe into the movie?

A:

Practically all time references in English are metaphoric. There are surprisingly few words that only refer to time: during, duration, durable, when, then, now, future, past. Most of the rest come from two major Metaphor Themes:

Time Is Money
spend a year, lose an hour, save ten minutes, cost me an hour, not worth the time
Time Is Space
before/after (fore/aft),  behind you/ahead of you, the months ahead/the following months

The use of into the movie (or into the meal, into the trip, etc. -- any noun designating an event with duration can be used here) is an example of the Motion in Space variant. 
The experiencer of duration is metaphorically moving through Time, which is represented as 3-dimensional space. Hence through and into are appropriate prepositions to refer to the durational constituents -- cohesive cognitive events like watching a movie or hearing a speech or doing a morning's work or conducting a career -- through is appropriate for an undifferentiated event (throughout my life in Denver), and in(to) for a timed event a specified "length" of time from the beginning. Metaphors are  unavoidable in language.
I.e, just as one says, 50 miles into the trip, one may say 50 minutes into the movie. 

