What is written on Agent Hanaway's ring and what is the meaning of it?
Wikipedia to the rescue. On its page "Mission: Impossible – Ghost Protocol", we have:
Bird, having directed several Disney and Pixar films and short films, incorporated the trademark "A113" into the movie on two separate occasions. The first is the design print on Agent Hanaway's ring during the flashback sequence, and the second being when Hunt calls in for support and uses the drop callsign, Alpha 1-1-3.
So, what is this "A113"? Again, Wikipedia is smart. Let's see the page "A113":
A113 (sometimes A-113 or A1-13) is an inside joke present as an Easter egg in animated films created by alumni of California Institute of the Arts, referring to the classroom number used by graphic design and character animation students at the school that was used by John Lasseter and Brad Bird among others. Brad Bird first used it for a license plate number in the "Family Dog" episode of Amazing Stories. It has since appeared in other Disney movies and every Pixar movie.