Every railroad's rolling stock carries a "roadname" identifier. In most cases, it's either three or four letters long. This is often an abbreviation of the railroad's name, although it may mean something else as well. Private carriers (i.e., they don't have their own rails) always ends in an "X". Underneath or next to this "roadname" will be the "road number", allowing every individual railcar to be easily identified by refering to its road name and road number.
Examples:
RDG - Reading (like you said)
BN - BUrlington Northern
ATSF - Santa Fe
MP - Missouri Pacific
ROCK - Rock Island (also CRIP)
MILW - Milwaukee Road
ICG - Illinois Central Gulf
They are also sometimes referred to as "reporting marks" - there are a number of websites on the internet that lists ALL of them (or a close approximation).
