There have been a very few rare instances where through a painter's error, there were two cars with identical initials and numbers. I vaguely recall seeing one such instance in an old RAILROAD magazine, and reading about another. This was back in the days of paper and pencil recordkeeping. Such a mistake would be far less likely to happen with today's computerized reporting.
About 25 years ago the shortline I was on received two cars with the same initial, but with 2 digits transposed. For example, 27548 and 27458. They were billed to two separate food processing plants. When the crew was done I found they had given the cars to the wrong customers because of the similarity. But as I was preparing to make panicked phone calls I looked at the waybills and saw that not only did each contain the same commodity from the same shipper, but the weights and quantity were identical. I called each plant and they agreed to just unload the car they had and call it even - which it was!