All MiG-15 aircraft had serial numbers which indicated the following: factory of production; factory production series number; one-up number within the series.
The most famous one, MiG-15bis #1315325, was the primary aircraft of Colonel HSU Yevgeniy Pepelyayev. That breaks out as Series 13, Factory No. 153, serial number 25. The "bort" (side) number used on the aircraft, #325, was well known to all of the Soviets, as well as its red nose and tail tip.
(Alas, while it survived the war and went back to the USSR it was inadvertently scrapped as its past career was still classified.)
There were six or seven other factories, and while all used slightly different schemes the idea was the same as was the information presented.
But US pilots never had to produce a serial number to get credit for a MiG claim, so the system ends there.